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Chapter 5Resource Masters
New York, New York Columbus, Ohio Woodland Hills, California Peoria, Illinois
StudentWorksTM This CD-ROM includes the entire Student Edition along with the Study Guide, Practice, and Enrichment masters.
TeacherWorksTM All of the materials found in this booklet are included for viewing and printing in the Advanced Mathematical Concepts TeacherWorksCD-ROM.
Copyright © The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Advanced Mathematical Concepts.Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill 8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-869132-X Advanced Mathematical ConceptsChapter 5 Resource Masters
1 2 3 4 5 6 7 8 9 10 XXX 11 10 09 08 07 06 05 04
© Glencoe/McGraw-Hill iii Advanced Mathematical Concepts
Vocabulary Builder . . . . . . . . . . . . . . . . . vii-x
Lesson 5-1Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 181Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Lesson 5-2Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 184Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Lesson 5-3Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 187Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Lesson 5-4Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 190Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Lesson 5-5Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 193Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Lesson 5-6Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 196Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Lesson 5-7Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 199Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Lesson 5-8Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . 202Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Chapter 5 AssessmentChapter 5 Test, Form 1A . . . . . . . . . . . . 205-206Chapter 5 Test, Form 1B . . . . . . . . . . . . 207-208Chapter 5 Test, Form 1C . . . . . . . . . . . . 209-210Chapter 5 Test, Form 2A . . . . . . . . . . . . 211-212Chapter 5 Test, Form 2B . . . . . . . . . . . . 213-214Chapter 5 Test, Form 2C . . . . . . . . . . . . 215-216Chapter 5 Extended Response
Assessment . . . . . . . . . . . . . . . . . . . . . . . 217Chapter 5 Mid-Chapter Test . . . . . . . . . . . . . 218Chapter 5 Quizzes A & B . . . . . . . . . . . . . . . 219Chapter 5 Quizzes C & D. . . . . . . . . . . . . . . 220Chapter 5 SAT and ACT Practice . . . . . 221-222Chapter 5 Cumulative Review . . . . . . . . . . . 223
SAT and ACT Practice Answer Sheet,10 Questions . . . . . . . . . . . . . . . . . . . . . . . A1
SAT and ACT Practice Answer Sheet,20 Questions . . . . . . . . . . . . . . . . . . . . . . . A2
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A3-A17
Contents
© Glencoe/McGraw-Hill iv Advanced Mathematical Concepts
A Teacher’s Guide to Using theChapter 5 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file theresources you use most often. The Chapter 5 Resource Masters include the corematerials needed for Chapter 5. These materials include worksheets, extensions,and assessment options. The answers for these pages appear at the back of thisbooklet.
All of the materials found in this booklet are included for viewing and printing inthe Advanced Mathematical Concepts TeacherWorks CD-ROM.
Vocabulary Builder Pages vii-x include a student study tool that presents the key vocabulary terms from the chapter. Students areto record definitions and/or examples for eachterm. You may suggest that students highlight orstar the terms with which they are not familiar.
When to Use Give these pages to studentsbefore beginning Lesson 5-1. Remind them toadd definitions and examples as they completeeach lesson.
Study Guide There is one Study Guide master for each lesson.
When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can alsobe used in conjunction with the Student Editionas an instructional tool for those students whohave been absent.
Practice There is one master for each lesson.These problems more closely follow the structure of the Practice section of the StudentEdition exercises. These exercises are ofaverage difficulty.
When to Use These provide additional practice options or may be used as homeworkfor second day teaching of the lesson.
Enrichment There is one master for eachlesson. These activities may extend the conceptsin the lesson, offer a historical or multiculturallook at the concepts, or widen students’perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for usewith all levels of students.
When to Use These may be used as extracredit, short-term projects, or as activities fordays when class periods are shortened.
© Glencoe/McGraw-Hill v Advanced Mathematical Concepts
Assessment Options
The assessment section of the Chapter 5Resources Masters offers a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessments
Chapter Tests• Forms 1A, 1B, and 1C Form 1 tests contain
multiple-choice questions. Form 1A isintended for use with honors-level students,Form 1B is intended for use with average-level students, and Form 1C is intended foruse with basic-level students. These testsare similar in format to offer comparabletesting situations.
• Forms 2A, 2B, and 2C Form 2 tests arecomposed of free-response questions. Form2A is intended for use with honors-levelstudents, Form 2B is intended for use withaverage-level students, and Form 2C isintended for use with basic-level students.These tests are similar in format to offercomparable testing situations.
All of the above tests include a challengingBonus question.
• The Extended Response Assessmentincludes performance assessment tasks thatare suitable for all students. A scoringrubric is included for evaluation guidelines.Sample answers are provided for assessment.
Intermediate Assessment• A Mid-Chapter Test provides an option to
assess the first half of the chapter. It iscomposed of free-response questions.
• Four free-response quizzes are included tooffer assessment at appropriate intervals inthe chapter.
Continuing Assessment• The SAT and ACT Practice offers
continuing review of concepts in variousformats, which may appear on standardizedtests that they may encounter. This practiceincludes multiple-choice, quantitative-comparison, and grid-in questions. Bubble-in and grid-in answer sections are providedon the master.
• The Cumulative Review provides studentsan opportunity to reinforce and retain skillsas they proceed through their study ofadvanced mathematics. It can also be usedas a test. The master includes free-responsequestions.
Answers• Page A1 is an answer sheet for the SAT and
ACT Practice questions that appear in theStudent Edition on page 341. Page A2 is ananswer sheet for the SAT and ACT Practicemaster. These improve students’ familiaritywith the answer formats they mayencounter in test taking.
• The answers for the lesson-by-lesson masters are provided as reduced pages withanswers appearing in red.
• Full-size answer keys are provided for theassessment options in this booklet.
primarily skillsprimarily conceptsprimarily applications
BASIC AVERAGE ADVANCED
Study Guide
Vocabulary Builder
Parent and Student Study Guide (online)
Practice
Enrichment
4
5
3
2
Five Different Options to Meet the Needs of Every Student in a Variety of Ways
1
© Glencoe/McGraw-Hill vi Advanced Mathematical Concepts
Chapter 5 Leveled Worksheets
Glencoe’s leveled worksheets are helpful for meeting the needs of everystudent in a variety of ways. These worksheets, many of which are foundin the FAST FILE Chapter Resource Masters, are shown in the chartbelow.
• Study Guide masters provide worked-out examples as well as practiceproblems.
• Each chapter’s Vocabulary Builder master provides students theopportunity to write out key concepts and definitions in their ownwords.
• Practice masters provide average-level problems for students who are moving at a regular pace.
• Enrichment masters offer students the opportunity to extend theirlearning.
© Glencoe/McGraw-Hill vii Advanced Mathematical Concepts
This is an alphabetical list of the key vocabulary terms you will learn in Chapter 5.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term.
Vocabulary Term Foundon Page Definition/Description/Example
ambiguous case
angle of depression
angle of elevation
apothem
arccosine relation
arcsine relation
arctangent relation
circular function
cofunctions
cosecant
(continued on the next page)
Reading to Learn MathematicsVocabulary Builder
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill viii Advanced Mathematical Concepts
Vocabulary Term Foundon Page Definition/Description/Example
cosine
cotangent
coterminal angles
degree
Hero’s Formula
hypotenuse
initial side
inverse
Law of Cosines
Law of Sines
leg
(continued on the next page)
Reading to Learn MathematicsVocabulary Builder (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill ix Advanced Mathematical Concepts
Reading to Learn MathematicsVocabulary Builder (continued)
NAME _____________________________ DATE _______________ PERIOD ________
3
Vocabulary Term Foundon Page Definition/Description/Example
minute
quadrant angle
reference angle
secant
second
side adjacent
side opposite
sine
solve a triangle
standard position
tangent
(continued on the next page)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill x Advanced Mathematical Concepts
Reading to Learn MathematicsVocabulary Builder (continued)
NAME _____________________________ DATE _______________ PERIOD ________
Vocabulary Term Foundon Page Definition/Description/Example
terminal side
trigonometric function
trigonometric ratio
unit circle
vertex
Chapter
5
© Glencoe/McGraw-Hill 181 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
5-1
Angles and Degree MeasureDecimal degree measures can be expressed in degrees(°),minutes(′), and seconds(″).
Example 1 a. Change 12.520° to degrees, minutes, andseconds.12.520° � 12° � (0.520 � 60)′ Multiply the decimal portion of
� 12° � 31.2′ the degrees by 60 to find minutes.� 12° � 31′ � (0.2 � 60)″ Multiply the decimal portion of� 12° � 31′ � 12″ the minutes by 60 to find seconds.
12.520° can be written as 12° 31′ 12″.
b. Write 24° 15′ 33″ as a decimal rounded to thenearest thousandth.
24° 15′ 33″ � 24° � 15′ ��610°′�� � 33″ ��36
10°0″��
� 24.259°24° 15′ 33″ can be written as 24.259°.
An angle may be generated by the rotation of one raymultiple times about the origin.
Example 2 Give the angle measure represented by eachrotation.a. 2.3 rotations clockwise
2.3 � �360 � �828 Clockwise rotations have negative measures.The angle measure of 2.3 clockwise rotations is �828°.
b. 4.2 rotations counterclockwise4.2 � 360 � 1512 Counterclockwise rotations have positive
measures.The angle measure of 4.2 counterclockwise rotations is 1512°.
If � is a nonquadrantal angle in standard position, its referenceangle is defined as the acute angle formed by the terminal side ofthe given angle and the x-axis.
Example 3 Find the measure of the reference angle for 220°.Because 220° is between 180° and 270°, theterminal side of the angle is in Quadrant III.220° � 180° � 40°The reference angle is 40°.
Reference
For any angle �, 0° < � < 360°, its reference angle �′ is defined by
Angle Rule
a. �, when the terminal side is in Quadrant I,b. 180° � �, when the terminal side is in Quadrant II,c. � � 180°, when the terminal side is in Quadrant III, andd. 360° � �, when the terminal side is in Quadrant IV.
© Glencoe/McGraw-Hill 182 Advanced Mathematical Concepts
Angles and Degree Measure
Change each measure to degrees, minutes, and seconds.1. 28.955� 2. �57.327�
Write each measure as a decimal degree to the nearestthousandth.
3. 32� 28′ 10″ 4. �73� 14′ 35″
Give the angle measure represented by each rotation.5. 1.5 rotations clockwise 6. 2.6 rotations counterclockwise
Identify all angles that are coterminal with each angle. Then findone positive angle and one negative angle that are coterminalwith each angle.
7. 43� 8. �30�
If each angle is in standard position, determine a coterminal anglethat is between 0� and 360�, and state the quadrant in which theterminal side lies.
9. 472� 10. �995�
Find the measure of the reference angle for each angle.11. 227� 12. 640�
13. Navigation For an upcoming trip, Jackie plans to sail fromSanta Barbara Island, located at 33� 28′ 32″ N, 119� 2′ 7″ W, toSanta Catalina Island, located at 33.386� N, 118.430� W. Writethe latitude and longitude for Santa Barbara Island as decimalsto the nearest thousandth and the latitude and longitude forSanta Catalina Island as degrees, minutes, and seconds.
PracticeNAME _____________________________ DATE _______________ PERIOD ________
5-1
Reading Mathematics: If and Only If StatementsIf p and q are interchanged in a conditional statement so that pbecomes the conclusion and q becomes the hypothesis, the new state-ment, q → p, is called the converse of p → q.
If p → q is true, q → p may be either true or false.
Example Find the converse of each conditional.a. p → q: All squares are rectangles. (true)
q → p: All rectangles are squares. (false)
b. p → q: If a function ƒ(x) is increasing on aninterval I, then for every a and b contained inI, ƒ(a) � ƒ(b) whenever a � b. (true)q → p: If for every a and b contained in an interval I,ƒ(a) � ƒ(b) whenever a � b then function ƒ(x) isincreasing on I. (true)
In Lesson 3-5, you saw that the two statements in Example 2 can becombined in a single statement using the words “if and only if.”
A function ƒ(x) is increasing on an interval I if and only if forevery a and b contained in I, ƒ(a) � ƒ(b) whenever a � b.
The statement “p if and only if q” means that p implies q andq implies p.
State the converse of each conditional. Then tell if the converse istrue or false. If it is true, combine the statement and its converseinto a single statement using the words “if and only if.”
1. All integers are rational numbers.
2. If for all x in the domain of a function ƒ(x), ƒ(�x) � �ƒ(x), thenthe graph of ƒ(x) is symmetric with respect to the origin.
3. If ƒ(x) and ƒ�1(x) are inverse functions, then [ ƒ ° ƒ�1](x) � [ ƒ�1 ° ƒ](x) � x.
© Glencoe/McGraw-Hill 183 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
5-1
© Glencoe/McGraw-Hill 184 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
5-2
Trigonometric Ratios in Right TrianglesThe ratios of the sides of right triangles can be used to definethe trigonometric ratios known as the sine, cosine, andtangent.
Example 1 Find the values of the sine, cosine, and tangentfor �A.
First find the length of B�C�.(AC)2 � (BC)2 � (AB)2 Pythagorean Theorem
102 � (BC)2 � 202 Substitute 10 for AC and 20 for AB.(BC)2 � 300
BC � �3�0�0� or 10�3� Take the square root of each side.Disregard the negative root.
Then write each trigonometric ratio.
sin A � �shidyepo
otpepnoussiete
� cos A � �sihdyepaotdejnaucesne
t� tan A � �s
siiddee
aodpp
jaocseintet�
sin A � �102�0
3�� or ��23�� cos A � �12
00� or �2
1� tan A � �101�0
3�� or �3�
Trigonometric ratios are often simplified but never written asmixed numbers.
Three other trigonometric ratios, called cosecant, secant,and cotangent, are reciprocals of sine, cosine, and tangent,respectively.
Example 2 Find the values of the six trigonometric ratios for �R.
First determine the length of the hypotenuse.(RT)2 � (ST)2 � (RS)2 Pythagorean Theorem
152 � 32 � (RS)2 RT � 15, ST � 3(RS)2 � 234
RS � �2�3�4� or 3�2�6� Disregard the negative root.
sin R � �shidyepo
otpepnoussiete
� cos R � �sihdyepaotdejnaucesne
t� tan R � �s
siiddee
aodpp
jaocseintet�
sin R � �3�
32�6�� or ��26
2�6�� cos R � �3�
152�6�� or �5�
262�6�� tan R � �1
35� or �5
1�
csc R � �shidyepo
otpepnoussiete� sec R � �si
hdyepaotdejnaucesne
t� cot R � �ssiidd
ee
aopdpjaocseitnet
�
csc R � �3�32�6�� or �2�6� sec R � �3�
152�6�� or ��5
2�6�� cot R � �135� or 5
© Glencoe/McGraw-Hill 185 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
Trigonometric Ratios in Right Triangles
Find the values of the sine, cosine, and tangent for each �B.
1. 2.
3. If tan � � 5, find cot �. 4. If sin � � �38�, f ind csc �.
Find the values of the six trigonometric ratios for each �S.
5. 6.
7. Physics Suppose you are traveling in a car when a beam of lightpasses from the air to the windshield. The measure of the angle of incidence is 55�, and the measure of the angle of refraction is 35� 15′. Use Snell’s Law, �s
siinn
�
�
r
i� � n, to f ind the index of refraction nof the windshield to the nearest thousandth.
5-2
© Glencoe/McGraw-Hill 186 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
5-2
Using Right Triangles to Find the Area of Another TriangleYou can find the area of a right triangle by using the formula
A � bh. In the formula, one leg of the right triangle can be used as
the base, and the other leg can be used as the height.
The vertices of a triangle can be represented on the coordinate planeby three ordered pairs. In order to find the area of a general triangle,you can encase the triangle in a rectangle as shown in the diagrambelow.
A rectangle is placed around the triangle so that the vertices of thetriangle all touch the sides of the rectangle.Example Find the area of a triangle whose vertices are
A(�1, 3), B(4, 8), and C(8, 5).Plot the points and draw the triangle. Encase the trianglein a rectangle whose sides are parallel to the axes, then find the coordinates of the vertices of the rectangle.
Area �ABC � area ADEF � area �ADB �area �BEC � area �CFA, where �ADB, �BEC,and �CFA are all right triangles.
Area �ABC � 5(9) � (5)(5) � (4)(3) � (2)(9)
� 17.5 square units
Find the area of the triangle having vertices with each set of coordinates.1. A(4, 6), B(–1, 2), C(6, –5) 2. A(–2, –4), B(4, 7), C(6, –1)3. A(4, 2), B(6, 9), C(–1, 4) 4. A(2, –3), B(6, –8), C(3, 5)
1�2
1�2
1�2
1�2
© Glencoe/McGraw-Hill 187 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
Trigonometric Functions on the Unit Circle
Example 1 Use the unit circle to find cot (�270°).
The terminal side of a �270° angle in standard position is the positive y-axis,which intersects the unit circle at (0, 1).By definition, cot (�270°) � �y
x� or �01�.
Therefore, cot (�270°) � 0.
Trigonometric sin � � �yr� cos � � �
xr� tan � � �
yx�
Functions of an Angle in csc � � �y
r� sec � � �x
r� cot � � �
xy�
Standard Position
Example 2 Find the values of the six trigonometric functionsfor angle � in standard position if a point withcoordinates (�9, 12) lies on its terminal side.
We know that x � �9 and y � 12. We need tofind r.
r � �x�2��� y�2� Pythagorean Theorem
r � �(��9�)2� �� 1�2�2� Substitute �9 for x and 12 for y.
r � �2�2�5� or 15 Disregard the negative root.
sin � � �1125� or �45� cos � � ��15
9� or ��35� tan � � ��12
9� or ��43�
csc � � �1152� or �54� sec � � �
�15
9� or ��53� cot � � ��129� or ��34�
Example 3 Suppose � is an angle in standard position whoseterminal side lies in Quadrant I. If cos � � �35�, find the values of the remaining five trigonometricfunctions of �.
r2 � x2 � y2 Pythagorean Theorem52 � 32 � y2 Substitute 5 for r and 3 for x.16 � y2
4 � y Take the square root of each side.
Since the terminal side of � lies in Quadrant I, y mustbe positive.
sin � � �45� tan � � �43�
csc � � �54� sec � � �35� cot � � �34�
5-3
© Glencoe/McGraw-Hill 188 Advanced Mathematical Concepts
Trigonometric Functions on the Unit Circle
Use the unit circle to find each value.1. csc 90� 2. tan 270� 3. sin (�90�)
Use the unit circle to find the values of the six trigonometricfunctions for each angle.4. 45�
5. 120�
Find the values of the six trigonometric functions for angle � instandard position if a point with the given coordinates lies on itsterminal side.6. (�1, 5) 7. (7, 0) 8. (�3, �4)
PracticeNAME _____________________________ DATE _______________ PERIOD ________
5-3
© Glencoe/McGraw-Hill 189 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
5-3
Areas of Polygons and CirclesA regular polygon has sides of equal length and angles of equal measure. A regular polygon can be inscribed in or circumscribed about a circle. For n-sided regular polygons, the following area formulas can be used.
Area of circle AC �� r2
Area of inscribed polygon AI � � sin
Area of circumscribed polygon AC � nr2 � tan
Use a calculator to complete the chart below for a unit circle (a circle of radius 1).
1.
2.
3.
4.
5.
6.
7.
8.
9. What number do the areas of the circumscribed and inscribed polygons seem to be approaching as the number of sides of the polygon increases?
180°�
n
360°�
n
nr2
�2
NumberArea of Area of Circle Area of Area of Polygon
of SidesInscribed less Circumscribed lessPolygon Area of Polygon Polygon Area of Circle
3 1.2990381 1.8425545 5.1961524 2.0545598
4
8
12
20
24
28
32
1000
© Glencoe/McGraw-Hill 190 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
5-4
Applying Trigonometric FunctionsTrigonometric functions can be used to solve problemsinvolving right triangles.
Example 1 If T � 45° and u � 20, find t to the nearest tenth.
From the figure, we know the measures of anangle and the hypotenuse. We want to know themeasure of the side opposite the given angle. Thesine function relates the side opposite the angleand the hypotenuse.
sin T � �ut� sin � �
shidyepo
otpepnoussiete
�
sin 45° � �2t0� Substitute 45° for T and 20 for u.
20 sin 45° � t Multiply each side by 20.14.14213562 � t Use a calculator.
Therefore, t is about 14.1.
Example 2 Geometry The apothem of a regular polygon is themeasure of a line segment from the center of thepolygon to the midpoint of one of its sides. Theapothem of a regular hexagon is 2.6 centimeters.Find the radius of the circle circumscribed aboutthe hexagon to the nearest tenth.
First draw a diagram. Let a be the anglemeasure formed by a radius and its adjacentapothem. The measure of a is 360° 12 or30°. Now we know the measures of an angleand the side adjacent to the angle.
cos 30° � �2r.6� cos � �
sihdyepaotdejnaucesne
t�
r cos 30° � 2.6 Multiply each side by r.
r � �co2s.360°� Divide each side by cos 30°.
r � 3.0022214 Use a calculator.
Therefore, the radius is about 3.0 centimeters.
© Glencoe/McGraw-Hill 191 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
Applying Trigonometric FunctionsSolve each problem. Round to the nearest tenth.1. If A � 55� 55′ and c � 16, find a.
2. If a � 9 and B � 49�, f ind b.
3. If B � 56� 48′ and c � 63.1, find b.
4. If B � 64� and b � 19.2, find a.
5. If b � 14 and A � 16�, f ind c.
6. Construction A 30-foot ladder leaning against the side of a house makes a 70� 5′ angle with the ground.a. How far up the side of the house does the
ladder reach?
b. What is the horizontal distance between thebottom of the ladder and the house?
7. Geometry A circle is circumscribed about a regular hexagon with an apothem of 4.8 centimeters.a. Find the radius of the circumscribed circle.
b. What is the length of a side of the hexagon?
c. What is the perimeter of the hexagon?
8. Observation A person standing 100 feet from the bottomof a cliff notices a tower on top of the cliff. The angle of elevation to the top of the cliff is 30�. The angle of elevationto the top of the tower is 58�. How tall is the tower?
5-4
© Glencoe/McGraw-Hill 192 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
5-4
Making and Using a HypsometerA hypsometer is a device that can be used to measure the height ofan object. To construct your own hypsometer, you will need a rectangular piece of heavy cardboard that is at least 7 cm by 10 cm,a straw, transparent tape, a string about 20 cm long, and a smallweight that can be attached to the string.
Mark off 1-cm increments along one short side and one long side ofthe cardboard. Tape the straw to the other short side. Then attachthe weight to one end of the string, and attach the other end of thestring to one corner of the cardboard, as shown in the figure below.The diagram below shows how your hypsometer should look.
To use the hypsometer, you will need to measure the distance fromthe base of the object whose height you are finding to where youstand when you use the hypsometer.
Sight the top of the object through the straw. Note where the free-hanging string crosses the bottom scale. Then use similar trianglesto find the height of the object.
1. Draw a diagram to illustrate how you can use similar trianglesand the hypsometer to find the height of a tall object.
Use your hypsometer to find the height of each of the following.
2. your school’s flagpole3. a tree on your school’s property4. the highest point on the front wall of your school building5. the goal posts on a football field6. the hoop on a basketball court7. the top of the highest window of your school building8. the top of a school bus9. the top of a set of bleachers at your school
10. the top of a utility pole near your school
© Glencoe/McGraw-Hill 193 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
5-5
Solving Right TrianglesWhen we know a trigonometric value of an angle but not thevalue of the angle, we need to use the inverse of thetrigonometric function.
Example 1 Solve tan x � �3�.
If tan x � �3�, then x is an angle whose tangentis �3�.
x � arctan �3�
From a table of values, you can determine that x equals 60°, 240°, or any angle coterminal withthese angles.
Example 2 If c � 22 and b � 12, find B.
In this problem, we know the side opposite theangle and the hypotenuse. The sine functionrelates the side opposite the angle and thehypotenuse.
sin B � �bc� sin � �shidyepo
otpepnoussiete
�
sin B � �1222� Substitute 12 for b and 22 for c.
B � sin�1��1222�� Definition of inverse
B � 33.05573115 or about 33.1°.
Example 3 Solve the triangle where b � 20 and c � 35, giventhe triangle above.
a2 � b2 � c2
a2 � 202 � 352
a � �8�2�5�a � 28.72281323
55.15009542 � B � 90B � 34.84990458
Therefore, a � 28.7, A � 55.2°, and B � 34.8°.
cos A � �bc�
cos A � �3250�
A � cos-1��3250��
A � 55.15009542
Trigonometric Function Inverse Trigonometric Relationy � sin x x � sin�1 y or x � arcsin yy � cos x x � cos�1 y or x � arccos yy � tan x x � tan�1 y or x � arctan y
© Glencoe/McGraw-Hill 194 Advanced Mathematical Concepts
Solving Right Triangles
Solve each equation if 0� � x � 360�.
1. cos x � ��22�� 2. tan x � 1 3. sin x � �2
1�
Evaluate each expression. Assume that all angles are in Quadrant I.
4. tan �tan�1 ��33��� 5. tan �cos�1 �23�� 6. cos �arcsin �1
53��
Solve each problem. Round to the nearest tenth.7. If q � 10 and s � 3, find S.
8. If r � 12 and s � 4, find R.
9. If q � 20 and r � 15, find S.
Solve each triangle described, given the triangle at the right.Round to the nearest tenth, if necessary.10. a � 9, B � 49�
11. A � 16�, c � 14
12. a � 2, b � 7
13. Recreation The swimming pool at Perris Hill Plunge is 50 feetlong and 25 feet wide. The bottom of the pool is slanted so thatthe water depth is 3 feet at the shallow end and 15 feet at thedeep end. What is the angle of elevation at the bottom of thepool?
PracticeNAME _____________________________ DATE _______________ PERIOD ________
5-5
© Glencoe/McGraw-Hill 195 Advanced Mathematical Concepts
NAME _____________________________ DATE _______________ PERIOD ________
Enrichment5-5
Disproving Angle TrisectionMost geometry texts state that it is impossible to trisect an arbitraryangle using only a compass and straightedge. This fact has beenknown since ancient times, but since it is usually stated withoutproof, some geometry students do not believe it. If the students setout to find a method for trisecting angles, they will probably try thefollowing method. It is based on the familiar construction whichallows a segment to be divided into any desired number of congruentsegments. You can use inverse trigonometric functions to show thatapplication of the method to the trisection of angles is not valid.
Given: � AClaim: � A can be trisected using the following method.
Method: Choose point C on one ray of � A .Through C construct a perpendicular to the other ray, intersecting it at B.Construct M and N, the points that divide C�B� into three congruent segments. Draw A�M� and A�N�, whichtrisect �CAB into the congruent angles�1, �2, and �3.
The proposed method has been used to construct the figure below.CM � MN � NB � 1. AB � 5. Follow the instructions to show thatthe three angles �1, �2, and �3, are not congruent. Find anglemeasures to the nearest tenth of a degree.
1. Express m�3 as the value of an inverse function.
2. Find the measure of �3.
3. Write m�MAB as the value of an inverse function.
4. Find the measure of �MAB.5. Find the measure of �2.6. Find m�CAB and use it to find m �1.7. Explain why the proposed method for trisecting an angle fails.
© Glencoe/McGraw-Hill 196 Advanced Mathematical Concepts
The Law of Sines
Given the measures of two angles and one side of a triangle,we can use the Law of Sines to find one unique solution forthe triangle.
Example 1 Solve � ABC if A � 30°, B � 100°, and a � 15.
First find the measure of �C.C � 180° � (30° � 100°) or 50°
Use the Law of Sines to find b and c.
�sina
A� � �sinb
B� �sinc
C� � �sina
A�
�sin15
30°� � �sinb100°� �sin
c50°� � �sin
1530°�
�15ssinin
3100°0°� � b c � �15
sisnin30
5°0°�
29.54423259 � b c � 22.98133329
Therefore, C � 50°, b � 29.5, and c � 23.0.
The area of any triangle can be expressed in terms of twosides of a triangle and the measure of the included angle.
Example 2 Find the area of �ABC if a � 6.8, b � 9.3, and C � 57°.
K � �12�ab sin C
K � �12�(6.8)(9.3) sin 57°
K � 26.51876336
The area of �ABC is about 26.5 square units.
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
5-6
Law of Sines �sin
aA
� � �sin
bB
� � �sin
cC
�
Area (K) of a Triangle K � �12
�bc sin A K � �12
�ac sin B K � �12
�ab sin C
© Glencoe/McGraw-Hill 197 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
The Law of Sines
Solve each triangle. Round to the nearest tenth.1. A � 38�, B � 63�, c � 15 2. A � 33�, B � 29�, b � 41
3. A � 150�, C � 20�, a � 200 4. A � 30�, B � 45�, a � 10
Find the area of each triangle. Round to the nearest tenth.5. c � 4, A � 37�, B � 69� 6. C � 85�, a � 2, B � 19�
7. A � 50�, b � 12, c � 14 8. b � 14, C � 110�, B � 25�
9. b � 15, c � 20, A � 115� 10. a � 68, c � 110, B � 42.5�
11. Street Lighting A lamppost tilts toward the sunat a 2� angle from the vertical and casts a 25-footshadow. The angle from the tip of the shadow to thetop of the lamppost is 45�. Find the length of thelamppost.
5-6
© Glencoe/McGraw-Hill 198 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
5-6
Triangle ChallengeA surveyor took the following measurements from two irregularly-shaped pieces of land. Some of the lengths and angle measurementsare missing. Find all missing lengths and angle measurements. Roundlengths to the nearest tenth and angle measurements to the nearestminute.
1.
2.
e
G
H
a
f
e
J
b
c
© Glencoe/McGraw-Hill 199 Advanced Mathematical Concepts
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
The Ambiguous Case for the Law of SinesIf we know the measures of two sides and a nonincluded angle of a triangle, three situations are possible: no triangle exists, exactly one triangle exists, or two triangles exist. A triangle with two solutions is called the ambiguous case.
Example Find all solutions for the triangleif a � 20, b � 30, and A � 40°. If no solutions exist, write none.
Since 40° � 90°, consider Case 1.b sin A � 30 sin 40°b sin A � 19.28362829Since 19.3 � 20 � 30, there are two solutions forthe triangle.Use the Law of Sines to find B.
�sin20
40°� � �si3n0B� �sin
aA� � �sin
bB�
sin B � �30 s2in0
40°�
B � sin�1��30 s2in0
40°��B � 74.61856831
So, B � 74.6°. Since we know there are two solutions,there must be another possible measurement for B.In the second case, B must be less than 180° andhave the same sine value. Since we know that if � � 90, sin � � sin (180 � �), 180° � 74.6° or 105.4°is another possible measure for B. Now solve thetriangle for each possible measure of B.
Solution I
C � 180° � (40° � 74.6°) or 65.4°
�sina
A� � �sinc
C�
�sin20
40°� � �sin 6c5.4°�
c � �20ssiinn
4605°.4°�
c � 28.29040558
One solution is B � 74.6°,C � 65.4°, and c � 28.3.
5-7
Solution II
C � 180° � (40° � 105.4°) or 34.6°
�sina
A� � �sinc
C�
�sin20
40°� � �sin 3c4.6°�
c � �20ssiinn
4304°.6°�
c � 17.66816088
Another solution is B � 105.4°,C � 34.6°, and c � 17.7.
Case 1: A � 90° for a, b, and Aa � b sin A no solutiona � b sin A one solutiona � b one solutionb sin A � a � b two solutions
Case 2: A � 90°a b no solutiona � b one solution
© Glencoe/McGraw-Hill 200 Advanced Mathematical Concepts
The Ambiguous Case for the Law of Sines
Determine the number of possible solutions for each triangle.
1. A � 42�, a � 22, b � 12 2. a � 15, b � 25, A � 85�
3. A � 58�, a � 4.5, b � 5 4. A � 110�, a � 4, c � 4
Find all solutions for each triangle. If no solutions exist, writenone. Round to the nearest tenth.
5. b � 50, a � 33, A � 132� 6. a � 125, A � 25�, b � 150
7. a � 32, c � 20, A � 112� 8. a � 12, b � 15, A � 55�
9. A � 42�, a � 22, b � 12 10. b � 15, c � 13, C � 50�
11. Property Maintenance The McDougalls plan to fence a triangular parcel of theirland. One side of the property is 75 feet in length. It forms a 38� angle with anotherside of the property, which has not yet been measured. The remaining side of theproperty is 95 feet in length. Approximate to the nearest tenth the length of fenceneeded to enclose this parcel of the McDougalls’ lot.
PracticeNAME _____________________________ DATE _______________ PERIOD ________
5-7
© Glencoe/McGraw-Hill 201 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
5-7
Spherical TrianglesSpherical trigonometry is an extension of plane trigonometry.Figures are drawn on the surface of a sphere. Arcs of greatcircles correspond to line segments in the plane. The arcs ofthree great circles intersecting on a sphere form a sphericaltriangle. Angles have the same measure as the tangent linesdrawn to each great circle at the vertex. Since the sides arearcs, they too can be measured in degrees.
Example Solve the spherical triangle given a � 72°, b � 105°, and c � 61°.
Use the Law of Cosines.
0.3090 � (–0.2588)(0.4848) � (0.9659)(0.8746) cos Acos A � 0.5143
A � 59°
–0.2588 � (0.3090)(0.4848) � (0.9511)(0.8746) cos Bcos B � –0.4912
B � 119°
0.4848 � (0.3090)(–0.2588) � (0.9511)(0.9659) cos Ccos C � 0.6148
C � 52°
Check by using the Law of Sines.
� � � 1.1
Solve each spherical triangle.
1. a � 56°, b � 53°, c � 94° 2. a � 110°, b � 33°, c � 97°
3. a � 76°, b � 110°, C � 49° 4. b � 94°, c � 55°, A � 48°
sin 61°����sin 52°
sin 105°����sin 119°
sin 72°����sin 59°
The sum of the sides of a spherical triangle is less than 360°.The sum of the angles is greater than 180° and less than 540°.The Law of Sines for spherical triangles is as follows.
� �
There is also a Law of Cosines for spherical triangles.cos a � cos b cos c � sin b sin c cos Acos b � cos a cos c � sin a sin c cos Bcos c � cos a cos b � sin a sin b cos C
sin c�sin C
sin b�sin B
sin a�sin A
© Glencoe/McGraw-Hill 202 Advanced Mathematical Concepts
The Law of CosinesWhen we know the measures of two sides of a triangle andthe included angle, we can use the Law of Cosines to findthe measure of the third side. Often times we will use boththe Law of Cosines and the Law of Sines to solve a triangle.
Example 1 Solve �ABC if B � 40°, a � 12, and c � 6.
b2 � a2 � c2 � 2ac cos B Law of Cosinesb2 � 122 � 62 � 2(12)(6) cos 40°b2 � 69.68960019b � 8.348029719
So, b � 8.3.
�sinb
B� � �sinc
C� Law of Sines
�sin8.
430°� � �sin
6C�
sin C � �6 si8n.3
40°�
C � sin�1��6 si8n.3
40°��C � 27.68859159
So, C � 27.7°.A � 180° � (40° � 27.7°) � 112.3°
The solution of this triangle is b � 8.3, A � 112.3°, and C � 27.7°.
Example 2 Find the area of �ABC if a � 5, b � 8, and c � 10.
First, find the semiperimeter of �ABC.s � �12�(a � b � c)
s � �12�(5 � 8 � 10)
s � 11.5
Now, apply Hero’s Formulak � �s(�s��� a�)(�s��� b�)(�s��� c�)�k � �1�1�.5�(1�1�.5� �� 5�)(�1�1�.5� �� 8�)(�1�1�.5� �� 1�0�)�k � �3�9�2�.4�3�7�5�k � 19.81003534
The area of the triangle is about 19.8 square units.
Study GuideNAME _____________________________ DATE _______________ PERIOD ________
5-8
a2 � b2 � c2 � 2bc cos ALaw of Cosines b2 � a2 � c2 � 2ac cos B
c2 � a2 � b2 � 2ab cos C
© Glencoe/McGraw-Hill 203 Advanced Mathematical Concepts
PracticeNAME _____________________________ DATE _______________ PERIOD ________
The Law of Cosines
Solve each triangle. Round to the nearest tenth.
1. a � 20, b � 12, c � 28 2. a � 10, c � 8, B � 100�
3. c � 49, b � 40, A � 53� 4. a � 5, b � 7, c � 10
Find the area of each triangle. Round to the nearest tenth.
5. a � 5, b � 12, c � 13 6. a � 11, b � 13, c � 16
7. a � 14, b � 9, c � 8 8. a � 8, b � 7, c � 3
9. The sides of a triangle measure 13.4 centimeters,18.7 centimeters, and 26.5 centimeters. Find the measureof the angle with the least measure.
10. Orienteering During an orienteering hike, two hikers start at point A and head in a direction 30� west of south to point B. They hike 6 miles from point A to point B. From point B, they hike to point C and then from point C back to point A, which is 8 miles directly north of point C. How many miles did they hike from point B to point C?
5-8
© Glencoe/McGraw-Hill 204 Advanced Mathematical Concepts
EnrichmentNAME _____________________________ DATE _______________ PERIOD ________
5-8
The Law of Cosines and the Pythagorean TheoremThe law of cosines bears strong similarities to thePythagorean Theorem. According to the Law ofCosines, if two sides of a triangle have lengths a andb and if the angle between them has a measure of x,then the length, y, of the third side of the trianglecan be found by using the equation
y2 � a2 � b2 � 2ab cos (x°).
Answer the following questions to clarify the relationship between the Law of Cosines and the Pythagorean Theorem.
1. If the value of x becomes less and less, what number is cos (x°)close to?
2. If the value of x is very close to zero but then increases, whathappens to cos (x°) as x approaches 90?
3. If x equals 90, what is the value of cos (x°)? What does the equa-tion of y2 � a2 � b2 � 2ab cos (x°) simplify to if x equals 90?
4. What happens to the value of cos (x°) as x increases beyond 90and approaches 180?
5. Consider some particular values of a and b, say 7 for a and19 for b. Use a graphing calculator to graph the equation youget by solving y2 � 72 � 192 � 2(7)(19) cos (x°) for y.
a. In view of the geometry of the situation, what range of valuesshould you use for X on a graphing calculator?
b. Display the graph and use the TRACE function. What do themaximum and minimum values appear to be for the function?
c. How do the answers for part b relate to the lengths 7 and 19?Are the maximum and minimum values from part b ever actually attained in the geometric situation?
© Glencoe/McGraw-Hill 205 Advanced Mathematical Concepts
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5 Chapter 5 Test, Form 1A
Write the letter for the correct answer in the blank at the right ofeach problem.
1. Change 128.433° to degrees, minutes, and seconds. 1. ________A. 128° 25′ 58″ B. 128° 25′ 59″ C. 128° 25′ 92″ D. 128° 26′ 00″
2. Write 43° 18′ 35″ as a decimal to the nearest thousandth of a degree. 2. ________A. 43.306° B. 43.308° C. 43.309° D. 43.310°
3. Give the angle measure represented by 3.25 rotations clockwise. 3. ________A. �1170° B. �90° C. 90° D. 1170°
4. Identify all coterminal angles between �360° and 360° 4. ________for the angle �420°.A. �60° and 300° B. �30° and 330°C. 30° and �330° D. 60° and �300°
5. Find the measure of the reference angle for 1046°. 5. ________A. �56° B. 56° C. 34° D. �34°
6. Find the value of the tangent for �A. 6. ________A. �2�
25�� B. ��2
5��
C. �23� D. ��35��
7. Find the value of the secant for �R. 7. ________A. ��5
7�0�� B. �3�14
1�4��
C. ��35�� D. ��3
1�4��
8. Which of the following is equal to csc θ ? 8. ________A. �sin
1θ� B. �co
1s θ� C. �ta
1n θ� D. �se
1c θ�
9. If cot θ � 0.85, find tan θ . 9. ________A. 0.588 B. 0.85 C. 1.176 D. 1.7
10. Find cos (�270°). 10. ________A. undefined B. �1 C. 1 D. 0
11. Find the exact value of sec 300°. 11. ________A. �2 B. ��2�
33�� C. 2 D. �2�
33��
12. Find the value of csc θ for angle θ in standard position if 12. ________the point at (5, �2) lies on its terminal side.A. ���2
2�9�� B. ��2�29
2�9�� C. ��52�9�� D. �5�
292�9��
13. Suppose θ is an angle in standard position whose terminal side 13. ________lies in Quadrant II. If sin θ � �11
23� , find the value of sec θ .
A. ��153� B. ��15
3� C. ��152� D. �1
123�
© Glencoe/McGraw-Hill 206 Advanced Mathematical Concepts
For Exercises 14 and 15, refer to the figure. The angle of elevation from the end of the shadow to the top of the building is 63° and the distance is 220 feet.
14. Find the height of the building to the nearest foot. 14. ________A. 100 ft B. 196 ftC. 432 ft D. 112 ft
15. Find the length of the shadow to the nearest foot. 15. ________A. 100 ft B. 196 ftC. 432 ft D. 112 ft
16. If 0° ≤ x ≤ 360°, solve the equation sec x � �2. 16. ________A. 150° and 210° B. 210° and 330°C. 120° and 240° D. 240° and 300°
17. Assuming an angle in Quadrant I, evaluate csc �cot�1 �43��. 17. ________
A. �35� B. �53� C. �45� D. �54�
18. Given the triangle at the right, find B to the 18. ________nearest tenth of a degree if b � 10 and c � 14.A. 44.4° B. 35.5°C. 54.5° D. 45.6°
For Exercises 19 and 20, round answers to the nearest tenth.19. In �ABC, A � 27° 35′, B � 78° 23′, and c � 19. Find a. 19. ________
A. 8.6 B. 9.2 C. 12.8 D. 19.4
20. If A � 42.2°, B � 13.6°, and a � 41.3, find the area of �ABC. 20. ________A. 138.8 units2 B. 493.8 units2 C. 327.4 units2 D. 246.9 units2
21. Determine the number of possible solutions if A � 62°, a � 4, 21. ________and b � 6.A. none B. one C. two D. three
22. Determine the greatest possible value for B if A � 30°, a � 5, 22. ________and b � 8.A. 23.1° B. 53.1° C. 126.9° D. 96.9°
For Exercises 23-25, round answers to the nearest tenth.23. In �ABC, A � 47°, b � 12, and c � 8. Find a. 23. ________
A. 6.3 B. 8.7 C. 8.8 D. 18.4
24. In �ABC, a � 7.8, b � 4.2, and c � 3.9. Find B. 24. ________A. 15.1° B. 148.7° C. 78.9° D. 16.2°
25. If a � 22, b � 14, and c � 30, find the area of �ABC. 25. ________A. 33 units2 B. 121.0 units2 C. 130.2 units2 D. 143.8 units2
Bonus The terminal side of an angle θ in standard position Bonus: ________coincides with the line 4x � y � 0 in Quadrant II. Find sec θto the nearest thousandth.
A. �0.243 B. �4.123 C. 0.243 D. 4.123
Chapter 5 Test, Form 1A (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill 207 Advanced Mathematical Concepts
Chapter 5 Test, Form 1B
NAME _____________________________ DATE _______________ PERIOD ________
Write the letter for the correct answer in the blank at the right ofeach problem.
1. Change 110.23° to degrees, minutes, and seconds. 1. ________A. 110° 13′ 00″ B. 110° 13′ 8″ C. 110° 13′ 28″ D. 110° 13′ 48″
2. Write 24° 38′ 42″ as a decimal to the nearest thousandth of a degree. 2. ________A. 24.645° B. 24.646° C. 24.647° D. 24.648°
3. Give the angle measure represented by 1.75 rotations counterclockwise. 3. ________A. �630° B. �90° C. 90° D. 630°
4. Identify the coterminal angle between �360° and 360° for the angle �120°. 4. ________A. �240° B. 60° C. 240° D. 300°
5. Find the measure of the reference angle for 295°. 5. ________A. 25° B. �65° C. �25° D. 65°
6. Find the value of the cosine for �A. 6. ________
A. �12� B. ��23��
C. ��33�� D. 2
7. Find the value of the cosecant for �R. 7. ________
A. ��26�� B. ��3
6��
C. ��31�5�� D. ��2
1�0��
8. Which of the following is equal to sec �? 8. ________A. �sin
1�
� B. �co1s �� C. �ta
1n �� D. �se
1c ��
9. If tan � � 0.25, find cot �. 9. ________A. 0.25 B. 4 C. 0.5 D. 14
10. Find cot (�180°). 10. ________A. undefined B. �1 C. 1 D. 0
11. Find the exact value of tan 240°. 11. ________A. ��3� B. ���
33�� C. �3� D. ��
33��
12. Find the value of sec � for angle � in standard position if the 12. ________point at (�2, �4) lies on its terminal side.A. ��2
5�� B. �5� C. ���25�� D. ��5�
13. Suppose � is an angle in standard position whose terminal side 13. ________lies in Quadrant III. If sin � � ��11
23�, find the value of cot �.
A. ��153� B. ��15
3� C. �152� D. �1
123�
Chapter
5
© Glencoe/McGraw-Hill 208 Advanced Mathematical Concepts
For Exercises 14 and 15, refer to the figure. The angleof elevation from the end of the shadow to the top ofthe building is 56° and the distance is 120 feet.14. Find the height of the building to the nearest foot. 14. ________
A. 99 ft B. 67 ftC. 178 ft D. 81 ft
15. Find the length of the shadow to the nearest foot. 15. ________A. 99 ft B. 67 ftC. 178 ft D. 81 ft
16. If 0° x 360°, solve the equation tan x � �1. 16. ________A. 135° and 315° B. 45° and 225° C. 45° and 315° D. 225° and 315°
17. Assuming an angle in Quadrant I, evaluate tan �cos�1 �45��. 17. ________
A. �34� B. �53� C. �45� D. �54�
18. Given the triangle at the right, find A to the nearest 18. ________tenth of a degree if b � 10 and c � 14.A. 44.4° B. 35.5°C. 54.5° D. 45.6°
For Exercises 19 and 20, round answers to the nearest tenth.19. In �ABC, A � 41° 15′, B � 107° 39′, and c � 19. Find b. 19. ________
A. 10.0 B. 24.3 C. 35.1 D. 54.6
20. If A � 52.6°, B � 49.8°, and a � 33.8, find the area of �ABC. 20. ________A. 117.9 units2 B. 338.2 units2 C. 536.4 units2 D. 1072.8 units2
21. Determine the number of possible solutions if A � 62°, a � 7, and b � 6. 21. ________A. none B. one C. two D. three
For Exercises 22–25, round answers to the nearest tenth.22. Determine the least possible value for B if A � 30°, a � 5, 22. ________
and b � 8.A. 23.1° B. 53.1° C. 126.9° D. 96.9°
23. In �ABC, B � 52°, a � 14, and c � 9. Find b. 23. ________A. 8.2 B. 11.0 C. 11.1 D. 18.4
24. In �ABC, a � 7.8, b � 4.2, and c � 3.9. Find A. 24. ________A. 15.1° B. 78.9° C. 148.7° D. 16.2°
25. If a � 32, b � 26, and c � 40, find the area of �ABC. 25. ________A. 49 units2 B. 121.0 units2 C. 298.6 units2 D. 415.2 units2
Bonus The terminal side of an angle � in standard position Bonus: ________coincides with the line 2x � y � 0 in Quadrant III.Find cos � to the nearest ten-thousandth.
A. �0.4472 B. 0.4472 C. �0.8944 D. 0.8944
Chapter 5 Test, Form 1B (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill 209 Advanced Mathematical Concepts
Chapter 5 Test, Form 1C
NAME _____________________________ DATE _______________ PERIOD ________
Write the letter for the correct answer in the blank at the right ofeach problem.
1. Change 36.3� to degrees, minutes, and seconds. 1. ________A. 36� 18′ 00″ B. 36� 18′ 16″ C. 36� 18′ 24″ D. 36� 18′ 28″
2. Write 21� 44′ 3″ as a decimal to the nearest thousandth of a degree. 2. ________A. 21.731� B. 21.732� C. 21.733� D. 21.734�
3. Give the angle measure represented by 0.5 rotation clockwise. 3. ________A. �180� B. �90� C. 90� D. 180�
4. Identify the coterminal angle between 0� and 360� for the angle 480�. 4. ________A. 30� B. 60� C. 120� D. 240�
5. Find the measure of the reference angle for 235�. 5. ________A. �125� B. 55� C. 25� D. �55�
6. Find the value of the sine for �A. 6. ________A. ��1�
51�9�� B. ��1
1�21�9��
C. �152� D. �15
2�
7. Find the value of the cotangent for �R. 7. ________A. �43� B. �4
3�
C. �45� D. �45�
8. Which of the following is equal to cot �? 8. ________A. �sin
1�
� B. �co1s �� C. �se
1c �� D. �tan
1�
�
9. If cos � � 0.5, find sec �. 9. ________A. 0.25 B. 0.5 C. 1 D. 2
10. Find tan 180�. 10. ________A. undefined B. �1 C. 1 D. 0
11. Find the exact value of cos 135�. 11. ________A. �1 B. ���2
2�� C. 1 D. ��22��
12. Find the value of csc � for angle � in standard position if the point at 12. ________(3, �1) lies on its terminal side.A. ��1�0� B. ���1
1�00�� C. ��3
1�0�� D. �3
13. Suppose � is an angle in standard position whose terminal side lies 13. ________in Quadrant II. If cos � � ��11
23�, find the value of tan �.
A. ��152� B. ��15
3� C. ��152� D. �1
123�
Chapter
5
© Glencoe/McGraw-Hill 210 Advanced Mathematical Concepts
For Exercises 14 and 15, refer to the figure. The angle of elevationfrom the end of the shadow to the top of the building is 70� andthe distance is 180 feet.14. Find the height of the building to the nearest foot. 14. ________
A. 62 ft B. 66 ftC. 169 ft D. 495 ft
15. Find the length of the shadow to the nearest foot. 15. ________A. 62 ft B. 66 ftC. 169 ft D. 495 ft
16. If 0� x 360�, solve the equation sin x � ���23��. 16. ________
A. 120� and 240� B. 240� and 300�C. 210� and 330� D. 150� and 210�
17. Assuming an angle in Quadrant I, evaluate cos �tan�1 �43��. 17. ________
A. �35� B. �53� C. �45� D. �45�
18. Given the triangle at the right, find B to the 18. ________nearest tenth of a degree if b � 8 and c � 12.A. 33.7� B. 41.8�C. 48.2� D. 56.3�
For Exercises 19 and 20, round answers to the nearest tenth.19. In �ABC, A � 102� 12�, B � 23� 21�, and c � 19.8. Find a. 19. ________
A. 8.0 B. 23.8 C. 48.8 D. 64.4
20. If A � 32.2�, b � 21.5, and c � 11.3, find the area of �ABC. 20. ________A. 129.5 units2 B. 102.8 units2 C. 64.7 units2 D. 32.6 units2
21. Determine the number of possible solutions if A � 48�, a � 5, and b � 6. 21. ________A. none B. one C. two D. three
22. Determine the least possible value for B if A � 20�, 22. ________a � 7, and b � 11.A. 12.6� B. 32.5� C. 147.5� D. 96.9�
For Exercises 23–25, round answers to the nearest tenth.23. In �ABC, A � 52�, b � 9, and c � 14. Find a. 23. ________
A. 6.3 B. 8.7 C. 8.8 D. 11.0
24. In �ABC, a � 2.4, b � 8.2, and c � 10.1. Find B. 24. ________A. 15.1� B. 21.7� C. 28.9� D. 33.3�
25. If a � 12, b � 30, and c � 22, find the area of �ABC. 25. ________A. 33.7 units2 B. 93.4 units2 C. 113.1 units2 D. 143.8 units2
Bonus The terminal side of an angle � in standard position Bonus: ________coincides with the line y � �12�x in Quadrant I. Find sin � to the nearest thousandth.
A. 0.233 B. 0.447 C. 0.508 D. 0.693
Chapter 5 Test, Form 1C (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill 211 Advanced Mathematical Concepts
Chapter 5 Test, Form 2A
NAME _____________________________ DATE _______________ PERIOD ________
1. Change 225.639� to degrees, minutes, and seconds. 1. __________________
2. Write 23� 16′ 25″ as a decimal to the nearest thousandth of a degree. 2. ____________________
3. State the angle measure represented by 2.4 rotations clockwise. 3. ____________________
4. Identify all coterminal angles between �360� and 360� for the 4. ____________________angle �540�.
5. Find the measure of the reference angle for 562�. 5. ____________________
6. Find the value of the sine for �A. 6. ____________________
7. Find the value of the cotangent for �A. 7. ____________________
8. Find the value of the secant for �A. 8. ____________________
9. If csc � � �2, find sin �. 9. ____________________
10. Find sin (�270�). 10. ____________________
11. Find the exact value of cot 330�. 11. ____________________
12. Find the exact value of sec � for angle � in standard position if 12. ____________________the point at (�3, 2) lies on its terminal side.
13. Suppose � is an angle in standard position whose terminal side 13. ____________________lies in Quadrant IV. If cos � � �11
23�, find the value of csc �.
Chapter
5
For Exercises 6–8, refer to the figure.
Exercises 6–8
© Glencoe/McGraw-Hill 212 Advanced Mathematical Concepts
For Exercises 14 and 15, refer to the figure. The angle of elevationfrom the far side of the pool to the top of the waterfall is 75�, andthe distance is 185 feet.14. Find the height of the waterfall 14. __________________
to the nearest foot.
15. Find the width across the pool 15.to the nearest foot.
16. If 0� x 360�, solve cot x � ��3�. 16. __________________
17. Assuming an angle in Quadrant I, evaluate sec �tan�1 �34��. 17. __________________
18. Given triangle at the right, 18. __________________find B to the nearest tenth of a degree if a � 8 and b � 20.
For Exercises 19 and 20, round answers to the nearest tenth.19. In �ABC, A � 47� 15′, B � 58� 33′, and c � 23. Find a. 19. __________________
20. If A � 37.2�, B � 17.9�, and a � 22.3, find the area of �ABC. 20. __________________
21. Determine the number of possible solutions if A � 47�, 21. __________________a � 4, and b � 5.
22. Determine the least possible value for c if A � 30�, 22. __________________a � 5, and b � 8.
For Exercises 23-25, round answers to the nearest tenth.23. In �ABC, A � 118�, b � 8, and c � 6. Find a. 23. __________________
24. In �ABC, a � 9, b � 5, and c � 12. Find B. 24. __________________
25. If a � 12, b � 24, and c � 30, find the area of �ABC. 25. __________________
Bonus The terminal side of an angle � in standard Bonus: __________________position coincides with the line 3x � y � 0 in Quadrant II. Find csc � to the nearest thousandth.
Chapter 5 Test, Form 2A (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill 213 Advanced Mathematical Concepts
Chapter 5 Test, Form 2B
NAME _____________________________ DATE _______________ PERIOD ________
1. Change 124.63° to degrees, minutes, and seconds. 1. __________________
2. Write 48° 32′ 15″ as a decimal to the nearest thousandth of 2. __________________a degree.
3. State the angle measure represented by 1.25 rotations 3. __________________clockwise.
4. Identify all coterminal angles between �360° and 360° for 4. __________________the angle 630°.
5. Find the measure of the reference angle for 310°. 5. __________________
6. Find the value of the cosine for �A. 6. __________________
7. Find the value of the cosecant for �A. 7. __________________
8. Find the value of the cotangent for �A. 8. __________________
9. If sec � � �4, find cos �. 9. __________________
10. Find tan (�180°). 10. __________________
11. Find the exact value of sec 240°. 11. __________________
12. Find the exact value of sec � for angle � in standard 12. __________________position if the point at (�4, 5) lies on its terminal side.
13. Suppose � is an angle in standard position whose terminal 13. __________________side lies in Quadrant IV. If cos � � �11
23�, find the value of cot �.
Chapter
5
Exercises 6–8
For Exercises 6–8, refer to the figure.
© Glencoe/McGraw-Hill 214 Advanced Mathematical Concepts
For Exercises 14 and 15, refer to the figure. The angle of elevationfrom the far side of the pool to the top of the waterfall is 54°, andthe distance is 230 feet.14. Find the height of the waterfall 14. __________________
to the nearest foot.
15. Find the width across the pool 15. __________________to the nearest foot.
16. If 0° x 360°, solve the equation csc x � �2. 16. __________________
17. Assuming an angle in Quadrant I, evaluate cos �cot�1 �152��. 17. __________________
18. Given the triangle at the right, 18. __________________find B to the nearest tenth of a degree if a � 12 and c � 22.
For Exercises 19 and 20, round answers to the nearest tenth.19. In �ABC, A � 42°, B � 68°, and c � 15. Find a. 19. __________________
20. If A � 27.2°, B � 67.4°, and a � 12.8, find the area of �ABC. 20. __________________
21. Determine the number of possible solutions if A � 110°, 21. __________________a � 5, and b � 4.
For Exercises 22–25, round answers to the nearest tenth.22. Determine the greatest possible value for c if A � 30°, 22. __________________
a � 5, and b � 8.
23. In �ABC, A � 59°, b � 12, and c � 4. Find a. 23. __________________
24. In �ABC, a � 4, b � 11, and c � 8. Find B. 24. __________________
25. If a � 21, b � 15, and c � 28, find the area of � ABC. 25. __________________
Bonus The terminal side of an angle � in standard Bonus: _________________position coincides with the line 3x � y � 0 in Quadrant III. Find sin � to the nearest ten-thousandth.
Chapter 5 Test, Form 2B (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill 215 Advanced Mathematical Concepts
Chapter 5 Test, Form 2C
NAME _____________________________ DATE _______________ PERIOD ________
1. Change 25.6� to degrees, minutes, and seconds. 1. __________________
2. Write 75� 30′ as a decimal to the nearest thousandth of a 2. __________________degree.
3. State the angle measure represented by 1.5 rotations 3. __________________counterclockwise.
4. Identify a coterminal angle between 0� and 360� for the 4. __________________angle �225�.
5. Find the measure of the reference angle for 235�. 5. __________________
6. Find the value of the sine for �A. 6. __________________
7. Find the value of the cotangent for �A. 7. __________________
8. Find the value of the secant for �A. 8. __________________
9. If tan � � �3, find cot �. 9. __________________
10. Find tan 180�. 10. __________________
11. Find the exact value of cos 330�. 11. __________________
12. Find the exact value of sin � for angle � in standard position 12. __________________if the point at (�1, 4) lies on its terminal side.
13. Suppose � is an angle in standard position whose 13. __________________terminal side lies in Quadrant II. If sin � � �11
23�, find
the value of sec �.
Chapter
5
Exercises 6–8
For Excercises 6–8, refer to the figure.
© Glencoe/McGraw-Hill 216 Advanced Mathematical Concepts
For Exercises 14 and 15, refer to the figure. The angle of elevationfrom the far side of the pool to the top of the waterfall is 68� andthe distance is 200 feet.14. Find the height of the waterfall 14. __________________
to the nearest foot.
15. Find the width across the pool 15.to the nearest foot.
16. If 0� x 360�, solve sin x � ���23��. 16. __________________
17. Assuming an angle in Quadrant I, evaluate cos �tan�1 �152��. 17. __________________
18. Given the triangle at the right, 18. __________________find B to the nearest tenth of a degree if b � 12 and c � 18.
For Exercises 19 and 20, round answers to the nearest tenth.19. In �ABC, A � 47�, B � 58�, and b � 23. Find a. 19. __________________
20. If C � 37.2�, a � 17.9, and b � 22.3, find the area of �ABC. 20. __________________
21. Determine the number of possible solutions if A � 47�, 21. __________________a � 2, and b � 4.
22. Determine the greatest possible value for c if A � 15�, 22. __________________a � 8, and b � 13.
For Exercises 23–25, round answers to the nearest tenth.23. In �ABC, A � 67�, b � 10, and c � 5. Find a. 23. __________________
24. In �ABC, a � 8, b � 6, and c � 12. Find C. 24. __________________
25. If a � 18, b � 22, and c � 30, find the area of �ABC. 25. __________________
Bonus The terminal side of an angle � in standard Bonus: __________________position coincides with the line y � x in Quadrant I. Find tan � to the nearest thousandth.
Chapter 5 Test, Form 2C (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
© Glencoe/McGraw-Hill 217 Advanced Mathematical Concepts
Chapter 5 Open-Ended Assessment
NAME _____________________________ DATE _______________ PERIOD ________
Instructions: Demonstrate your knowledge by giving a clear,concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond therequirements of the problem.
1. The point at (�3, ��3�) lies on the terminal side of an angle in standard position.
a. Give the degree measure of three angles that fit the description.
b. Tell how to find the cosine of such angles. Give the cosine of these angles.
c. Name angles in the first, second, and fourth quadrants that have the same reference angle as those above.
d. Write the coordinates of a point in Quadrant II. Find the values of the six trigonometric functions of an angle in standard position with this point on its terminal side.
2. A children’s play area is being built next to a circular fountain in the park. A fence will be erected around the play area for safety. A diagram of the area is shown below.
a. How long will the fence need to be in order to enclose the area?
b. The park commission is planning to enlarge the play area. Do you think it should be enlarged to the east or to the west? Why?
Chapter
5
© Glencoe/McGraw-Hill 218 Advanced Mathematical Concepts
Chapter 5 Mid-Chapter Test (Lessons 5-1 through 5-4)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
51. Change 65.782� to degrees, minutes, and seconds. 1. __________________
2. If a �470� angle is in standard position, determine a 2. __________________coterminal angle that is between 0� and 360�. State the quadrant in which the terminal side lies.
For Exercises 3 and 4, use right triangle ABC to find each value.
3. Find the value of the cosine for �A. 3. __________________
4. Find the value of the cotangent for �A. 4. __________________
5. If csc � � �3, find sin �. 5. __________________
6. Use the unit circle to find tan 180�. 6. __________________
7. Find the exact value of sin 300�. 7. __________________
8. Find the value of csc � for angle � in standard position if 8. __________________the point at (2, �1) lies on its terminal side.
For Exercises 9 and 10, use right triangle ABC to find each value to the nearest tenth.
9. Find b. 9. __________________
10. Find c. 10. __________________
1. Change 47.283� to degrees, minutes, and seconds. 1. __________________2. Write 122� 43′ 12″ as a decimal to the nearest thousandth 2. __________________
of a degree.3. Give the angle measure represented by 2.25 rotations 3. __________________
counterclockwise.4. Identify all coterminal angles between �360� and 360� 4. __________________
for the angle 480�.5. Find the measure of the reference angle for 323�. 5. __________________6. Find the value of the sine for �A. 6. __________________7. Find the value of the tangent for �A. 7. __________________8. Find the value of the secant for �A. 8. __________________
9. If cot � � ��23�, find tan �. 9. __________________
10. If sin � � 0.5, find csc �. 10. __________________
Use the unit circle to find each value. 1. __________________
1. sin (�90�) 2. csc 180� 2. __________________3. Find the exact value of cos 210�. 3. __________________4. Find the exact value of tan 135�. 4. __________________5. Find the value of sec � for angle � in standard position if 5. __________________
the point at (4, �5) lies on its terminal side.6. Suppose � is an angle in standard position whose terminal 6. __________________
side lies in Quadrant III. If tan � � �152�, find the value of sin �.
Refer to the figure. Find each value to the nearest tenth.
7. Find a. 7. __________________8. Find c. 8. __________________
A 100-foot cable is stretched from a stake in the ground to the topof a pole. The angle of elevation is 57°.
9. Find the height of the pole to the nearest tenth. 9. __________________10. Find the distance from the base of the pole to the 10. __________________
stake to the nearest tenth.
Chapter 5, Quiz B (Lessons 5-3 and 5-4)
NAME _____________________________ DATE _______________ PERIOD ________
Chapter 5, Quiz A (Lessons 5-1 and 5-2)
NAME _____________________________ DATE _______________ PERIOD ________
© Glencoe/McGraw-Hill 219 Advanced Mathematical Concepts
Chapter
5
Chapter
5
Exercises 6–8
1. If 0� x 360�, solve: csc x � �2. 1. __________________
2. Assuming an angle in Quadrant I, evaluate tan �sec�1 �153��. 2. __________________
3. Given right triangle ABC, find B to the 3. __________________nearest tenth of a degree if b � 7 and c � 12.
Find each value. Round to the nearest tenth.4. In �ABC, A � 58� 21�, C � 97� 07�, and b � 23.8. Find a. 4. __________________
5. If B � 29.5�, C � 64.5�, and a � 18.8, find the area of �ABC. 5. __________________
1. Determine the number of possible solutions for �ABC 1. __________________if A � 28�, a � 4, and b � 11.
Find each value. Round to the nearest tenth.
2. For �ABC, determine the least possible value for B 2. __________________if A � 49�, a � 12, and b � 15.
3. In �ABC, B � 32�, a � 11, and c � 2.4. Find b. 3. __________________
4. In �ABC, a � 3.1, b � 5.4, and c � 4.7. Find C. 4. __________________
5. If a � 28.2, b � 36.5, and c � 40.1, find the area of �ABC. 5. __________________
Chapter 5, Quiz D (Lessons 5-7 and 5-8)
NAME _____________________________ DATE _______________ PERIOD ________
Chapter 5, Quiz C (Lessons 5-5 and 5-6)
NAME _____________________________ DATE _______________ PERIOD ________
© Glencoe/McGraw-Hill 220 Advanced Mathematical Concepts
Chapter
5
Chapter
5
© Glencoe/McGraw-Hill 221 Advanced Mathematical Concepts
Chapter 5 SAT and ACT Practice
NAME _____________________________ DATE _______________ PERIOD ________
After working each problem, record thecorrect answer on the answer sheetprovided or use your own paper.
Multiple Choice1. The length of a diagonal of a square
is 6 units. Find the length of a side.A 9�2� unitsB �2� unitsC 9 unitsD 3�2� unitsE None of these
2. If the area of �ABC is 30 square meters,what is the length of segment CD?A 2 mB 3 m C 5 mD 8 mE 10 m
3. The midpoint of a diameter of a circle is(3, 4). If the coordinates of one endpointof the diameter are (�3, 6), what arethe coordinates of the other endpoint?A (9, 2)B (9, 1) C (8, 2)D (3, 2)E (9, 14)
4. The endpoints of a diameter of a circleare (3, 2) and (11, 8). Find the area ofthe circle.A 5 units2
B 25 units2
C 25� units2
D 10� units2
E 5� units2
5. What is the arithmetic mean of �13� and �14�?A �16� B �7
1�
C �112� D �1
72�
E �274�
6. Which of the following products has thegreatest value less than 100?
A 2 � 4 � 6B 2 � 4 � 9C 4 � 4 � 9D 3 � 3 � 9E 4 � 4 � 6
7. A diagonal of a rectangle is �1�5�inches. The length of the rectangle is�1�2� inches. Find the area of the rectangle.A 3�2� in2
B 6 in2
C 9 in2
D 6�5� in2
E None of these
8. The diagonals of a rhombus are perpendicular and bisect each other.If the length of one side of a rhombus is 25 meters and the length of onediagonal is 14 meters, find the lengthof the other diagonal.A 7 mB 12 mC 24 mD 48 mE 144 m
9. If c � �a1b�, what is the value of a when
c � 12�1 and b � 3?A �36B ��3
16�
C �4D 4E None of these
10. How many times do the graphs of y � x2 and xy � 27 intersect?A 0B 1C 2D 3E 4
Chapter
5
© Glencoe/McGraw-Hill 222 Advanced Mathematical Concepts
Chapter 5 SAT and ACT Practice (continued)
NAME _____________________________ DATE _______________ PERIOD ________Chapter
5
7 and 12 8 and 11
11. If �143x� is an integer, then the value of x
CANNOT be which of the following?A �112B �32C 0D 6E 8
12. Which of the following statementsmakes the expression a � b representa negative number?A b � aB a � bC b � 0D a � 0E b � a
13. A hiker travels 5 miles due north, then3 miles due west, and then 2 miles duenorth. How far is the hiker from hisbeginning point?A About 8.2 miB About 7.1 miC About 9.4 miD About 6 miE About 7.6 mi
14. A rectangular swimming pool is 100 meters long and 25 meters wide.Lucia swims from one corner of thepool to the opposite corner and back10 times. How far did she swim?A About 193.6 mB About 1030.8 mC About 2061.6 mD About 10,308.8 mE None of these
15. 4 � 3�2� is a root of which equation?A x2 � 8x � 2 � 0B x2 � 8x � 18 � 0C x2 � 16x � 2 � 0D x2 � 16x � 18 � 0E None of these
16. If ƒ(x) � x4 � 4x3 � 16x � 16 has azero of �2, with a multiplicity of 3,what is another zero of ƒ?A 3B 2C �1D 1E 8
17–18. Quantitative ComparisonA if the quantity of Column A is
greaterB if the quantity in Column B is
greaterC if the two quantities are equalD if the relationship cannot be
determined from the informationgiven
Column A Column B17. The value of x in each figure
18. The length of the hypotenuse of aright triangle with the given leglengths
19. Grid-In A tent with a rectangularfloor has a diagonal length of 7 feetand a width of 5 feet. What is the areaof the floor to the nearest square foot?
20. Grid-In Julio wants to bury a waterpipe from one corner of his field to theopposite corner. How many feet ofpipe, to the nearest foot, does he needif the rectangular field is 200 feet by300 feet?
© Glencoe/McGraw-Hill 223 Advanced Mathematical Concepts
Chapter 5, Cumulative Review (Chapters 1-5)
NAME _____________________________ DATE _______________ PERIOD ________
1. If ƒ(x) � x � 2 and g(x) � �21x� , find g( ƒ(x)). 1. __________________
2. Determine whether the graphs of 2x � y � 5 � 0 2. __________________and x � 2y � 6 are parallel, coinciding, perpendicular, or none of these.
3. Graph the inequality 2x � 4y 8. 3.
4. Solve the following system of equations algebraically. 4. __________________5x � y � 162x � 3y � 3
5. Find BC if B � � � and C � � �. 5. __________________
6. Find the inverse of � �, if it exists. 6. __________________
7. Determine whether the graph of y � 2x4 � x2 � 3 is 7. __________________symmetric to the x-axis, the y-axis, both, or neither.
8. Describe the transformations relating the graph of 8. __________________y � ��x � 2� � 5 to its parent function, y � �x �.
9. Find the inverse of y � 2x � 6. State whether the inverse 9. __________________is a function.
10. Solve x2 � 6x � 6 � 0. 10. __________________
11. Solve �3
x� �� 2� � 7 � 4. 11. __________________
12. Find csc (�90°). 12. __________________
13. Given the right triangle ABC, 13.find side c to the nearest tenth.
14. In �ABC, a � 8, b � 6, and c � 10. Find B to the 14. __________________nearest tenth.
�13
24
5�4
�38
�25
61
Chapter
5
Blank
© Glencoe/McGraw-Hill A1 Advanced Mathematical Concepts
SAT and ACT Practice Answer Sheet(10 Questions)
NAME _____________________________ DATE _______________ PERIOD ________
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
© Glencoe/McGraw-Hill A2 Advanced Mathematical Concepts
SAT and ACT Practice Answer Sheet(20 Questions)
NAME _____________________________ DATE _______________ PERIOD ________
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
© G
lenc
oe/M
cGra
w-H
ill18
2A
dva
nced
Mat
hem
atic
al C
once
pts
An
gle
s a
nd
De
gre
e M
ea
sure
Ch
ang
e ea
ch m
easu
re t
o d
egre
es, m
inu
tes,
an
d s
econ
ds.
1.28
.955
�2.
�57
.327
�
28�
57′1
8″�
57�
19′3
7.2″
Wri
te e
ach
mea
sure
as
a d
ecim
al d
egre
e to
th
e n
eare
stth
ousa
nd
th.
3.32
�28
′10″
4.�
73�
14′3
5″32
.469
��
73.2
43�
Giv
e th
e an
gle
mea
sure
rep
rese
nte
d b
y ea
ch r
otat
ion
.5.
1.5
rota
tion
s cl
ockw
ise
6.2.
6 ro
tati
ons
cou
nte
rclo
ckw
ise
�54
0�93
6�
Iden
tify
all
ang
les
that
are
cot
erm
inal
wit
h e
ach
an
gle
. Th
en f
ind
one
pos
itiv
e an
gle
an
d o
ne
neg
ativ
e an
gle
th
at a
re c
oter
min
alw
ith
eac
h a
ng
le.
7.43
�8.
�30
�
43�
�36
0k�;
�30
��
360k
�;sa
mp
le a
nsw
ers:
sam
ple
ans
wer
s:76
3�;�
317�
690�
;�75
0�
If e
ach
an
gle
is in
sta
nd
ard
pos
itio
n, d
eter
min
e a
cote
rmin
al a
ng
leth
at is
bet
wee
n 0
�an
d 3
60�,
an
d s
tate
th
e q
uad
ran
t in
wh
ich
th
ete
rmin
al s
ide
lies.
9.47
2�10
.�
995�
112�
; II
85�;
I
Fin
d t
he
mea
sure
of
the
refe
ren
ce a
ng
le f
or e
ach
an
gle
.11
.227
�12
.64
0�47
�80
�
13.N
avi
gati
onF
or a
n u
pcom
ing
trip
, Jac
kie
plan
s to
sai
l fro
mS
anta
Bar
bara
Isl
and,
loca
ted
at 3
3�28
′32″
N, 1
19�
2′7″
W, t
oS
anta
Cat
alin
a Is
lan
d, lo
cate
d at
33.
386�
N, 1
18.4
30�
W. W
rite
the
lati
tude
an
d lo
ngi
tude
for
San
ta B
arba
ra I
slan
d as
dec
imal
sto
th
e n
eare
st t
hou
san
dth
an
d th
e la
titu
de a
nd
lon
gitu
de f
orS
anta
Cat
alin
a Is
lan
d as
deg
rees
, min
ute
s, a
nd
seco
nds
.S
anta
Bar
bar
a Is
land
: 33.
476�
N, 1
19.0
35�
WS
anta
Cat
alin
a Is
land
: 33�
23′9
.6″
N, 1
18�
25′4
8″W
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
5-1
Answers (Lesson 5-1)
© Glencoe/McGraw-Hill A3 Advanced Mathematical Concepts
Re
ad
ing
Ma
the
ma
tic
s: I
f a
nd
On
ly I
f S
tate
me
nts
If p
an
d q
are
inte
rch
ange
d in
a c
ondi
tion
al s
tate
men
t so
th
at p
beco
mes
th
e co
ncl
usi
on a
nd
q be
com
es t
he
hyp
oth
esis
, th
e n
ewst
atem
ent,
q →
p, is
cal
led
the
con
vers
eof
p →
q.
If p
→q
is t
rue,
q →
pm
ay b
e ei
ther
tru
e or
fal
se.
Exa
mp
leF
ind
th
e co
nve
rse
of e
ach
con
dit
ion
al.
a.p
→q
: All
sq
uar
es a
re r
ecta
ngl
es.
(tru
e)q
→p:
All
rec
tan
gles
are
squ
ares
.(f
alse
)
b.
p→
q: I
f a
fun
ctio
n ƒ
(x)
is i
ncr
easi
ng
on a
nin
terv
al I
, th
en f
or e
very
aan
d b
con
tain
ed i
nI,
ƒ(a
)�
ƒ(b)
wh
enev
er a
�b.
(tru
e)q
→p:
If
for
ever
y a
and
bco
nta
ined
in a
n in
terv
al I
,ƒ(
a)�
ƒ(b)
wh
enev
era
�b
then
fu
nct
ion
ƒ(x
) is
incr
easi
ng
on I
.(t
rue)
In L
esso
n 3
-5, y
ou s
aw t
hat
th
e tw
o st
atem
ents
in E
xam
ple
2 ca
n b
eco
mbi
ned
in a
sin
gle
stat
emen
t u
sin
g th
e w
ords
“if
an
d on
ly if
.”
Afu
nct
ion
ƒ(x
) is
incr
easi
ng
on a
n in
terv
al I
if
and
on
ly i
ffo
rev
ery
aan
d b
con
tain
ed in
I, ƒ
(a)�
ƒ(b)
wh
enev
era
�b.
Th
e st
atem
ent
“p if
an
d on
ly if
q”
mea
ns
that
p im
plie
s q
and
q im
plie
s p.
Sta
te t
he
con
vers
e of
eac
h c
ond
itio
nal
. T
hen
tel
l if
the
con
vers
e is
tru
e or
fal
se.
If it
is t
rue,
com
bin
e th
e st
atem
ent
and
its
con
vers
ein
to a
sin
gle
sta
tem
ent
usi
ng
th
e w
ord
s “i
f an
d o
nly
if.”
1.A
ll in
tege
rs a
re r
atio
nal
nu
mbe
rs.
All
rati
ona
l num
ber
s ar
e in
teg
ers;
fal
se2.
If f
or a
ll x
in t
he
dom
ain
of
a fu
nct
ion
ƒ(x
), ƒ
(�x)
��
ƒ(x)
, th
enth
e gr
aph
of
ƒ(x)
is s
ymm
etri
c w
ith
res
pect
to
the
orig
in.
If a
fun
ctio
n ha
s a
gra
ph
that
is s
ymm
etri
c w
ith
resp
ect
toth
e o
rig
in, t
hen
ƒ(�
x)�
�ƒ
(x) f
or
all x
in t
he d
om
ain
of
ƒ(x
);tr
ue. A
fun
ctio
n ha
s a
gra
ph
that
is s
ymm
etri
c w
ith
resp
ect
to t
he o
rig
in if
and
onl
y if
ƒ(�
x)�
�ƒ
(x) f
or
all x
in t
hed
om
ain
of
ƒ(x
).3.
If ƒ
(x)
and
ƒ�1 (
x) a
re in
vers
e fu
nct
ion
s, t
hen
[ƒ
°ƒ�
1 ](x
)�[ƒ
�1
°ƒ
](x)
�x.
If [
ƒ °
ƒ�
1 ](x
)�[ƒ
�1
°ƒ
](x)
�x,
the
n ƒ
(x) a
nd ƒ
�1 (
x) a
re in
vers
e fu
ncti
ons
; tru
e. T
wo
fun
ctio
ns, ƒ
(x) a
nd ƒ
�1 (
x), a
re in
vers
e fu
ncti
ons
if a
nd o
nly
if [ƒ
°ƒ
�1 ]
(x)�
[ƒ�
1°
ƒ](
x)�
x.
© G
lenc
oe/M
cGra
w-H
ill18
3A
dva
nced
Mat
hem
atic
al C
once
pts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
5-1
Answers (Lesson 5-2)
© Glencoe/McGraw-Hill A4 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill18
5A
dva
nced
Mat
hem
atic
al C
once
pts
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
Trig
on
om
etr
ic R
atio
s in
Rig
ht
Tria
ng
les
Fin
d t
he
valu
es o
f th
e si
ne,
cos
ine,
an
d t
ang
ent
for
each
�B
.
1.2.
sin
B�
�3 8� ; co
s B
���
85�5� �;
sin
B�
�2�5
5��
; co
s B
��� 55� �
;
tan
B�
�3�55
5�5� �ta
n B
�2
3.If
tan
��
5, f
ind
cot
�.
4.If
sin
��
�3 8� , f
ind
csc
�.
�1 5��8 3�
Fin
d t
he
valu
es o
f th
e si
x tr
igon
omet
ric
rati
os f
or e
ach
�S
.
5.6.
sin
S�
�3�10
1�0� �; c
os
S�
�� 11� 00 ��
;si
n S
�� 17 9�
; co
s S
��2�
197�8� �
;
tan
S�
3; c
sc S
���
31�0� �;
tan
S�
�7 1� 57� 68 ��
; csc
S�
�1 79 �;
sec
S�
�1 �0�
; co
t S
��1 3�
sec
S�
�191� 56
7�8��
; co
t S
��2�
77�8� �
7.P
hys
ics
Su
ppos
e yo
u a
re t
rave
lin
g in
a c
ar w
hen
a b
eam
of
ligh
tpa
sses
fro
m t
he
air
to t
he
win
dsh
ield
. Th
e m
easu
re o
f th
e an
gle
of in
cide
nce
is 5
5�, a
nd
the
mea
sure
of
the
angl
e of
ref
ract
ion
is
35�
15′.
Use
Sn
ell’s
Law
, �ss ii nn
�� ri�
�n
,to
fin
d th
e in
dex
of r
efra
ctio
n n
of t
he
win
dsh
ield
to
the
nea
rest
th
ousa
ndt
h.
abo
ut 1
.419
5-2
© G
lenc
oe/M
cGra
w-H
ill18
6A
dva
nced
Mat
hem
atic
al C
once
pts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
5-2
Usi
ng
Rig
ht
Tria
ng
les
to F
ind
th
e A
rea
of
An
oth
er
Tria
ng
leYo
u c
an f
ind
the
area
of
a ri
ght
tria
ngl
e by
usi
ng
the
form
ula
A�
bh. I
n t
he
form
ula
, on
e le
g of
th
e ri
ght
tria
ngl
e ca
n b
e u
sed
as
the
base
, an
d th
e ot
her
leg
can
be
use
d as
th
e h
eigh
t.
Th
e ve
rtic
es o
f a
tria
ngl
e ca
n b
e re
pres
ente
d on
th
e co
ordi
nat
e pl
ane
by t
hree
ord
ered
pai
rs. I
n or
der
to fi
nd t
he a
rea
of a
gen
eral
tri
angl
e,yo
u c
an e
nca
seth
e tr
ian
gle
in a
rec
tan
gle
as s
how
n in
th
e di
agra
mbe
low
.
Are
ctan
gle
is p
lace
d ar
oun
d th
e tr
ian
gle
so t
hat
th
e ve
rtic
es o
f th
etr
ian
gle
all t
ouch
th
e si
des
of t
he
rect
angl
e.E
xam
ple
Fin
d t
he
area
of
a tr
ian
gle
wh
ose
vert
ices
are
A
(�1,
3),
B(4
, 8),
an
d C
(8, 5
).P
lot
the
poin
ts a
nd d
raw
the
tri
angl
e. E
ncas
e th
e tr
iang
lein
a r
ecta
ngl
e w
hos
e si
des
are
para
llel
to
the
axes
, th
en f
ind
the
coor
din
ates
of
the
vert
ices
of
the
rect
angl
e.
Are
a�
AB
C�
area
AD
EF
�ar
ea�
AD
B�
area
�B
EC
�ar
ea �
CFA
, wh
ere
�A
DB
,�
BE
C,
and
�C
FAar
e al
l rig
ht
tria
ngl
es.
Are
a�
AB
C�
5(9)
�(5
)(5)
�(4
)(3)
�(2
)(9)
�17
.5 s
quar
e u
nit
s
Fin
d t
he
area
of
the
tria
ng
le h
avin
g v
erti
ces
wit
h e
ach
set
of
coor
din
ates
.1.
A(4
, 6),
B(–
1, 2
), C
(6, –
5)31
.52.
A(–
2, –
4), B
(4, 7
), C
(6, –
1)35
3.A
(4, 2
), B
(6, 9
), C
(–1,
4)
19.5
4.A
(2, –
3), B
(6, –
8), C
(3, 5
)18
.5
1 � 21 � 2
1 � 2
1 � 2
Answers (Lesson 5-3)
© Glencoe/McGraw-Hill A5 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill18
9A
dva
nced
Mat
hem
atic
al C
once
pts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
5-3
Are
as
of
Po
lyg
on
s a
nd
Cir
cle
sA
regu
lar
poly
gon
has
sid
es o
f eq
ual
len
gth
an
d an
gles
of
equ
al
mea
sure
. A
regu
lar
poly
gon
can
be
insc
ribe
d in
or
circ
um
scri
bed
abou
t a
circ
le.
For
n-s
ided
reg
ula
r po
lygo
ns,
th
e fo
llow
ing
area
fo
rmu
las
can
be
use
d.
Are
a of
cir
cle
AC
��
r2
Are
a of
insc
ribe
d po
lygo
nA
I�
�si
n
Are
a of
cir
cum
scri
bed
poly
gon
AC
�n
r2�
tan
Use
a c
alcu
lato
r to
com
ple
te t
he
char
t b
elow
for
a u
nit
cir
cle
(a c
ircl
e of
rad
ius
1).
1. 2. 3. 4. 5. 6. 7. 8. 9.W
hat
nu
mbe
r do
th
e ar
eas
of t
he
circ
um
scri
bed
and
insc
ribe
d po
lygo
ns
seem
to
be a
ppro
ach
ing
as t
he
nu
mbe
r of
sid
es o
f th
e po
lygo
n in
crea
ses?
�
180°
�n
360°
�n
nr2
�2
Num
ber
Are
a o
fA
rea
of
Cir
cle
Are
a o
fA
rea
of
Po
lyg
on
of
Sid
esIn
scri
bed
less
Cir
cum
scri
bed
less
Po
lyg
on
Are
a o
f P
oly
go
nP
oly
go
nA
rea
of
Cir
cle
31.
2990
381
1.84
2554
55.
1961
524
2.05
4559
8
42
1.14
1592
74
0.85
8407
3
82.
8284
271
0.31
3165
53.
3137
085
0.17
2115
8
123
0.14
1592
73.
2153
903
0.07
3797
7
203.
0901
699
0.05
1422
73.
1676
888
0.02
6096
2
243.
1058
285
0.03
5764
13.
1596
599
0.01
8067
3
283.
1152
931
0.02
6299
63.
1548
423
0.01
3249
7
323.
1214
452
0.02
0147
53.
1517
249
0.01
0132
3
1000
3.14
1572
00.
0000
207
3.14
1603
00.
0000
103
© G
lenc
oe/M
cGra
w-H
ill18
8A
dva
nced
Mat
hem
atic
al C
once
pts
Trig
on
om
etr
ic F
un
ctio
ns
on
th
e U
nit C
irc
le
Use
th
e u
nit
cir
cle
to f
ind
eac
h v
alu
e.1.
csc
90�
2.ta
n 2
70�
3.si
n (
�90
�)1
und
efin
ed�
1
Use
th
e u
nit
cir
cle
to f
ind
th
e va
lues
of
the
six
trig
onom
etri
cfu
nct
ion
s fo
r ea
ch a
ng
le.
4.45
�
sin
45�
��� 22� �
csc
45�
��
2�
cos
45�
��� 22� �
sec
45�
��
2�
tan
45�
�1
cot
45�
�1
5.12
0�si
n 12
0��
�� 23� �cs
c 12
0��
�2�3
3��
cos
120�
��
�1 2�se
c 12
0��
�2
tan
120�
��
�3�
cot
120�
��
�� 33� �
Fin
d t
he
valu
es o
f th
e si
x tr
igon
omet
ric
fun
ctio
ns
for
ang
le �
inst
and
ard
pos
itio
n if
a p
oin
t w
ith
th
e g
iven
coo
rdin
ates
lies
on
its
term
inal
sid
e.6.
(�1,
5)
7.(7
, 0)
8.(�
3,�
4)
sin
��
�5�26
2�6� �si
n �
�0
sin
��
��4 5�
cos
��
��� 22� 66 �
�co
s �
�1
cos
��
��3 5�
tan
��
�5
tan
��
0ta
n �
�� 34 �
csc
��
��52�6� �
csc
��
und
efin
ed
csc
��
��5 4�
sec
��
��
2�6�se
c �
�1
sec
��
��5 3�
cot
��
��1 5�
cot
��
und
efin
edco
t �
�� 43 �
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
5-3
Answers (Lesson 5-4)
© Glencoe/McGraw-Hill A6 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill19
1A
dva
nced
Mat
hem
atic
al C
once
pts
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
Ap
ply
ing
Tri
go
no
me
tric
Fu
nc
tio
ns
Sol
ve e
ach
pro
ble
m. R
oun
d t
o th
e n
eare
st t
enth
.1.
If A
�55
�55
′an
d c
�16
, fin
d a.
13.3
2.If
a�
9 an
d B
�49
�, f
ind
b.10
.4
3.If
B�
56�
48′a
nd
c�
63.1
, fin
d b.
52.8
4.If
B�
64�
and
b�
19.2
, fin
d a.
9.4
5.If
b�
14 a
nd
A�
16�,
fin
d c.
14.6
6.C
onst
ruct
ion
A30
-foo
t la
dder
lean
ing
agai
nst
th
e si
de o
f a
hou
se m
akes
a 7
0�5′
angl
e w
ith
th
e gr
oun
d.a.
How
far
up
the
side
of
the
hou
se d
oes
the
ladd
er r
each
?ab
out
28.
2 ft
b.
Wh
at is
th
e h
oriz
onta
l dis
tan
ce b
etw
een
th
ebo
ttom
of
the
ladd
er a
nd
the
hou
se?
abo
ut 1
0.2
ft
7.G
eom
etry
Aci
rcle
is c
ircu
msc
ribe
d ab
out
a re
gula
r h
exag
on w
ith
an
ap
oth
em o
f 4.
8 ce
nti
met
ers.
a.F
ind
the
radi
us
of t
he
circ
um
scri
bed
circ
le.
abo
ut 5
.5 c
m
b.
Wh
at is
th
e le
ngt
h o
f a
side
of
the
hex
agon
?ab
out
5.5
cm
c.W
hat
is t
he
peri
met
er o
f th
e h
exag
on?
abo
ut 3
3 cm
8.O
bser
vati
onA
pers
on s
tan
din
g 10
0 fe
et f
rom
th
e bo
ttom
of a
cli
ff n
otic
es a
tow
er o
n t
op o
f th
e cl
iff.
Th
e an
gle
of
elev
atio
n t
o th
e to
p of
th
e cl
iff
is 3
0�. T
he
angl
e of
ele
vati
onto
th
e to
p of
th
e to
wer
is 5
8�. H
ow t
all i
s th
e to
wer
?ab
out
102
.3 f
t
5-4
© G
lenc
oe/M
cGra
w-H
ill19
2A
dva
nced
Mat
hem
atic
al C
once
pts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
5-4
Ma
kin
g a
nd
Usi
ng
a H
yp
som
ete
rA
hyp
som
eter
is a
dev
ice
that
can
be
use
d to
mea
sure
th
e h
eigh
t of
an o
bjec
t. T
o co
nst
ruct
you
r ow
n h
ypso
met
er, y
ou w
ill n
eed
a re
ctan
gula
r pi
ece
of h
eavy
car
dboa
rd t
hat
is a
t le
ast
7 cm
by
10 c
m,
a st
raw
, tra
nsp
aren
t ta
pe, a
str
ing
abou
t 20
cm
lon
g, a
nd
a sm
all
wei
ght
that
can
be
atta
ched
to
the
stri
ng.
Mar
k of
f 1-
cm in
crem
ents
alo
ng
one
shor
t si
de a
nd
one
lon
g si
de o
fth
e ca
rdbo
ard.
Tap
e th
e st
raw
to
the
oth
er s
hor
t si
de. T
hen
att
ach
the
wei
ght
to o
ne
end
of t
he
stri
ng,
an
d at
tach
th
e ot
her
en
d of
th
est
rin
g to
on
e co
rner
of
the
card
boar
d, a
s sh
own
in t
he
figu
re b
elow
.T
he
diag
ram
bel
ow s
how
s h
ow y
our
hyp
som
eter
sh
ould
look
.
To u
se t
he
hyp
som
eter
, you
wil
l nee
d to
mea
sure
th
e di
stan
ce f
rom
the
base
of
the
obje
ct w
hos
e h
eigh
t yo
u a
re f
indi
ng
to w
her
e yo
ust
and
wh
en y
ou u
se t
he
hyp
som
eter
.
Sig
ht
the
top
of t
he
obje
ct t
hro
ugh
th
e st
raw
. Not
e w
her
e th
e fr
ee-
han
gin
g st
rin
g cr
osse
s th
e bo
ttom
sca
le. T
hen
use
sim
ilar
tri
angl
esto
fin
d th
e h
eigh
t of
th
e ob
ject
.
1.D
raw
a d
iagr
am t
o il
lust
rate
how
you
can
use
sim
ilar
tri
angl
esan
d th
e h
ypso
met
er t
o fi
nd
the
hei
ght
of a
tal
l obj
ect.
See
stu
den
ts’ d
iag
ram
s.U
se y
our
hyp
som
eter
to
fin
d t
he
hei
gh
t of
eac
h o
f th
e fo
llow
ing
.
2.yo
ur
sch
ool’s
fla
gpol
e3.
a tr
ee o
n y
our
sch
ool’s
pro
pert
y4.
the
hig
hes
t po
int
on t
he
fron
t w
all o
f yo
ur
sch
ool b
uil
din
g5.
the
goal
pos
ts o
n a
foo
tbal
l fie
ld6.
the
hoo
p on
a b
aske
tbal
l cou
rt7.
the
top
of t
he
hig
hes
t w
indo
w o
f yo
ur
sch
ool b
uil
din
g8.
the
top
of a
sch
ool b
us
9.th
e to
p of
a s
et o
f bl
each
ers
at y
our
sch
ool
10.t
he
top
of a
uti
lity
pol
e n
ear
you
r sc
hoo
l
See
stu
den
ts’ w
ork
.
Answers (Lesson 5-5)
© Glencoe/McGraw-Hill A7 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill19
5A
dva
nced
Mat
hem
atic
al C
once
pts
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
Enr
ichm
ent
5-5
Dis
pro
vin
g A
ng
le T
rise
ctio
nM
ost
geom
etry
tex
ts s
tate
th
at it
is im
poss
ible
to
tris
ect
an a
rbit
rary
angl
e u
sin
g on
ly a
com
pass
an
d st
raig
hte
dge.
Th
is f
act
has
bee
nkn
own
sin
ce a
nci
ent
tim
es, b
ut
sin
ce it
is u
sual
ly s
tate
d w
ith
out
proo
f, s
ome
geom
etry
stu
den
ts d
o n
ot b
elie
ve it
. If
th
e st
ude
nts
set
out
to f
ind
a m
eth
od f
or t
rise
ctin
g an
gles
, th
ey w
ill p
roba
bly
try
the
foll
owin
g m
eth
od.
It is
bas
ed o
n t
he
fam
ilia
r co
nst
ruct
ion
wh
ich
allo
ws
a se
gmen
t to
be
divi
ded
into
an
y de
sire
d n
um
ber
ofco
ngr
uen
tse
gmen
ts.
You
can
use
inve
rse
trig
onom
etri
c fu
nct
ion
s to
sh
ow t
hat
appl
icat
ion
of
the
met
hod
to
the
tris
ecti
on o
f an
gles
is n
ot v
alid
.
Giv
en:
�A
Cla
im:
�A
can
be
tris
ecte
d u
sin
g th
e fo
llow
ing
met
hod
.M
eth
od:
Ch
oose
poi
nt
Con
on
e ra
y of
�A
.T
hro
ugh
Cco
nst
ruct
a p
erpe
ndi
cula
r to
th
e ot
her
ray
, in
ters
ecti
ng
it a
t B
. C
onst
ruct
M a
nd
N, t
he
poin
ts t
hat
di
vide
C�B�
into
th
ree
con
gru
ent
segm
ents
. D
raw
A �M�
and
A�N�
, wh
ich
tris
ect
�C
AB
into
th
e co
ngr
uen
t an
gles
�1,
�2,
an
d �
3.
Th
e pr
opos
ed m
eth
od h
as b
een
use
d to
con
stru
ct t
he
figu
re b
elow
.C
M�
MN
�N
B�
1. A
B�
5. F
ollo
w t
he
inst
ruct
ion
s to
sh
ow t
hat
the
thre
e an
gles
�1,
�2,
an
d �
3, a
re n
ot c
ongr
uen
t. F
ind
angl
em
easu
res
to t
he
nea
rest
ten
th o
f a
degr
ee.
1. E
xpre
ss m
�3
as t
he
valu
e of
an
inve
rse
fun
ctio
n.
m�
3�
Arc
tan
2.F
ind
the
mea
sure
of
�3.
m�
3�
11.3
°3.
Wri
te m
�M
AB
as
the
valu
e of
an
inve
rse
fun
ctio
n.
m�
MA
B�
Arc
tan
4.F
ind
the
mea
sure
of
�M
AB
.m
�M
AB
�21
.8°
5.F
ind
the
mea
sure
of
�2.
m�
2�
10.5
°6.
Fin
d m
�C
AB
and
use
it t
o fi
nd
m �
1.m
�1
�9.
2°7.
Exp
lain
wh
y th
e pr
opos
ed m
eth
od f
or t
rise
ctin
g an
an
gle
fail
s.T
he t
ang
ent
func
tio
n is
no
t lin
ear.
The
rat
io o
f th
e m
easu
res
of
two
ang
les
is n
ot
equa
l to
the
rat
io o
f th
e ta
ngen
ts o
f th
ean
gle
s.
2 � 5
1 � 5
© G
lenc
oe/M
cGra
w-H
ill19
4A
dva
nced
Mat
hem
atic
al C
once
pts
So
lvin
g R
igh
t Tr
ian
gle
s
Sol
ve e
ach
eq
uat
ion
if 0
��
x�
360
�.
1.co
s x
��� 22� �
2.ta
n x
�1
3.si
n x
�� 21 �
45�,
315
�45
�, 2
25�
30�,
150
�
Eva
luat
e ea
ch e
xpre
ssio
n. A
ssu
me
that
all
ang
les
are
in Q
uad
ran
t I.
4.ta
n �ta
n�
1�� 33� �
�5.
tan
�cos
�1
�2 3� �6.
cos �ar
csin
� 15 3��
�� 33 � ��� 25� �
� 11 32 �
Sol
ve e
ach
pro
ble
m. R
oun
d t
o th
e n
eare
st t
enth
.7.
If q
�10
an
d s
�3,
fin
d S
.17
.5�
8.If
r�
12 a
nd
s�
4, f
ind
R.
71.6
�
9.If
q�
20 a
nd
r�
15, f
ind
S.
41.4
�
Sol
ve e
ach
tri
ang
le d
escr
ibed
, giv
en t
he
tria
ng
le a
t th
e ri
gh
t.R
oun
d t
o th
e n
eare
st t
enth
, if
nec
essa
ry.
10.a
�9,
B�
49�
A�
41�,
b�
10.4
, c�
13.7
11.
A�
16�,
c�
14a
�3.
9, b
�13
.5, B
�74
�
12.a
�2,
b�
7c
�7.
3, A
�15
.9�,
B�
74.1
�
13.R
ecre
ati
onT
he
swim
min
g po
ol a
t P
erri
s H
ill P
lun
ge is
50
feet
lon
g an
d 25
fee
t w
ide.
Th
e bo
ttom
of
the
pool
is s
lan
ted
so t
hat
the
wat
er d
epth
is 3
fee
t at
th
e sh
allo
w e
nd
and
15 f
eet
at t
he
deep
en
d. W
hat
is t
he
angl
e of
ele
vati
on a
t th
e bo
ttom
of
the
pool
?ab
out
13.
5�
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
5-5
Answers (Lesson 5-6)
© Glencoe/McGraw-Hill A8 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill19
8A
dva
nced
Mat
hem
atic
al C
once
pts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
5-6
Tria
ng
le C
ha
lle
ng
eA
surv
eyor
too
k th
e fo
llow
ing
mea
sure
men
ts f
rom
tw
o ir
regu
larl
y-sh
aped
pie
ces
of la
nd.
Som
e of
th
e le
ngt
hs
and
angl
e m
easu
rem
ents
are
mis
sin
g. F
ind
all m
issi
ng
len
gth
s an
d an
gle
mea
sure
men
ts.
Rou
nd
len
gth
s to
th
e n
eare
st t
enth
an
d an
gle
mea
sure
men
ts t
o th
en
eare
st m
inu
te.
1.
a �
66.7
;b
�52
.7; e
�49
.5A
�10
3°58
';B
�50
°8';
D�
76°8
';E
�50
°52'
;G
�76
°52'
; H�
54°8
'
2.
b�
113.
4; c
�11
0.8;
e �
52.3
;f
�40
.5;
A�
32°3
7';
;C
�71
°23'
; D�
55°3
7';
E�
82°2
3'; J
�10
0°
e
G
H
a
f
e
J
b
c
© G
lenc
oe/M
cGra
w-H
ill19
7A
dva
nced
Mat
hem
atic
al C
once
pts
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
Th
e L
aw
of
Sin
es
Sol
ve e
ach
tri
ang
le. R
oun
d t
o th
e n
eare
st t
enth
.1.
A�
38�,
B�
63�,
c�
152.
A�
33�,
B�
29�,
b�
41C
�79
�, a
�9.
4, b
�13
.6C
�11
8�, a
�46
.1, c
�74
.7
3.A
�15
0�, C
�20
�, a
�20
04.
A�
30�,
B�
45�,
a�
10B
�10
�, b
�69
.5,
C�
105�
, b�
14.1
, c�
19.3
c�
136.
8
Fin
d t
he
area
of
each
tri
ang
le. R
oun
d t
o th
e n
eare
st t
enth
.5.
c�
4, A
�37
�, B
�69
�6.
C�
85�,
a�
2, B
�19
�
4.7
unit
s20.
7 un
its2
7.A
�50
�, b
�12
, c�
148.
b�
14, C
�11
0�, B
�25
�
64.3
uni
ts2
154.
1 un
its2
9.b
�15
,c�
20, A
�11
5�10
.a
�68
, c�
110,
B�
42.5
�
135.
9 un
its2
2526
.7 u
nits
2
11.
Str
eet
Lig
hti
ng
Ala
mpp
ost
tilt
s to
war
d th
e su
nat
a 2
�an
gle
from
th
e ve
rtic
al a
nd
cast
s a
25-f
oot
shad
ow. T
he
angl
e fr
om t
he
tip
of t
he
shad
ow t
o th
eto
p of
th
e la
mpp
ost
is 4
5�. F
ind
the
len
gth
of
the
lam
ppos
t.ab
out
25.
9 ft
5-6
Answers (Lesson 5-7)
© Glencoe/McGraw-Hill A9 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill20
1A
dva
nced
Mat
hem
atic
al C
once
pts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
5-7
Sp
he
ric
al Tr
ian
gle
sS
pher
ical
tri
gon
omet
ry is
an
ext
ensi
on o
f pl
ane
trig
onom
etry
.F
igu
res
are
draw
n o
n t
he
surf
ace
of a
sph
ere.
Arc
s of
gre
atci
rcle
s co
rres
pon
d to
lin
e se
gmen
ts in
th
e pl
ane.
Th
e ar
cs o
fth
ree
grea
t ci
rcle
s in
ters
ecti
ng
on a
sph
ere
form
a s
pher
ical
tria
ngl
e. A
ngl
es h
ave
the
sam
e m
easu
re a
s th
e ta
nge
nt
lin
esdr
awn
to
each
gre
at c
ircl
e at
th
e ve
rtex
. S
ince
th
e si
des
are
arcs
, th
ey t
oo c
an b
e m
easu
red
in d
egre
es.
Exa
mp
leS
olve
th
e sp
her
ical
tri
angl
e gi
ven
a�
72°,
b�
105°
, an
d c
�61
°.
Use
th
e L
aw o
f C
osin
es.
0.30
90�
(–0.
2588
)(0.
4848
)�(0
.965
9)(0
.874
6) c
os A
cos
A�
0.51
43A
�59
°
–0.2
588
� (0
.309
0)(0
.484
8)�
(0.9
511)
(0.8
746)
cos
Bco
s B
�–
0.49
12B
�11
9°
0.48
48�
(0.3
090)
(–0.
2588
)�(0
.951
1)(0
.965
9) c
os C
cos
C�
0.61
48C
�52
°
Ch
eck
by u
sin
g th
e L
aw o
f S
ines
.
��
�1.
1
Sol
ve e
ach
sp
her
ical
tri
ang
le.
1. a
�56
°, b
�53
°, c
�94
°2.
a�
110°
, b�
33°,
c�
97°
A�
41°,
B�
39°,
C�
128°
A�
116°
, B�
31°,
C�
71°
3. a
�76
°, b
�11
0°, C
�49
°4.
b�
94°,
c�
55°,
A�
48°
A�
59°,
B�
124°
, c�
59°
a�
60°,
B�
121°
, C�
45°
sin
61°
��
��
sin
52°
sin
105
°�
��
�si
n 1
19°
sin
72°
��
��
sin
59°
The
sum
of t
he s
ides
of a
sph
eric
al tr
iang
le is
less
than
360
°.T
he s
um o
f the
ang
les
is g
reat
er th
an 1
80°
and
less
than
540
°.T
he L
aw o
f Sin
es fo
r sp
heric
al tr
iang
les
is a
s fo
llow
s.
��
The
re is
als
o a
Law
of C
osin
es fo
r sp
heric
al tr
iang
les.
cos
a�
cos
bco
s c
�si
n b
sin
cco
s A
cos
b�
cos
aco
s c
�si
n a
sin
cco
s B
cos
c�
cos
aco
s b
�si
n a
sin
bco
s C
sin
c� si
nC
sin
b� si
n B
sin
a� si
nA
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0A
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nced
Mat
hem
atic
al C
once
pts
Th
e A
mb
igu
ou
s C
ase
fo
r th
e L
aw
of
Sin
es
Det
erm
ine
the
nu
mb
er o
f p
ossi
ble
sol
uti
ons
for
each
tri
ang
le.
1.A
�42
�, a
�22
, b�
122.
a�
15, b
�25
, A�
85�
10
3.A
�58
�, a
�4.
5, b
�5
4.A
�11
0�, a
�4,
c�
42
0
Fin
d a
ll so
luti
ons
for
each
tri
ang
le. I
f n
o so
luti
ons
exis
t, w
rite
non
e. R
oun
d t
o th
e n
eare
st t
enth
.
5.b
�50
, a�
33, A
�13
2�6.
a�
125,
A�
25�,
b�
150
none
B�
30.5
�, C
�12
4.5�
, c�
243.
7;B
�14
9.5�
, C�
5.5�
, c�
28.3
7.a
�32
, c�
20, A
�11
2�8.
a�
12, b
�15
, A�
55�
B�
32.6
�, C
�35
.4�,
no
neb
�18
.6
9.A
�42
�, a
�22
, b�
1210
.b
�15
, c�
13, C
�50
�
B�
21.4
�, C
�11
6.6�
, A
�67
.9�,
B�
62.1
�, a
�15
.7;
c�
29.4
A�
12.1
�, B
�11
7.9�
, a�
3.6
11.
Pro
per
ty M
ain
ten
an
ceT
he
McD
ouga
lls
plan
to
fen
ce a
tri
angu
lar
parc
el o
f th
eir
lan
d. O
ne
side
of
the
prop
erty
is 7
5 fe
et in
len
gth
. It
form
s a
38�
angl
e w
ith
an
oth
ersi
de o
f th
e pr
oper
ty, w
hic
h h
as n
ot y
et b
een
mea
sure
d. T
he
rem
ain
ing
side
of
the
prop
erty
is 9
5 fe
et in
len
gth
. App
roxi
mat
e to
th
e n
eare
st t
enth
th
e le
ngt
h o
f fe
nce
nee
ded
to e
ncl
ose
this
par
cel o
f th
e M
cDou
gall
s’lo
t.
abo
ut 3
12.1
ft
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
5-7
Answers (Lesson 5-8)
© Glencoe/McGraw-Hill A10 Advanced Mathematical Concepts
© G
lenc
oe/M
cGra
w-H
ill20
4A
dva
nced
Mat
hem
atic
al C
once
pts
Enr
ichm
ent
NA
ME
____
____
____
____
____
____
____
_ D
ATE
____
____
____
___
PE
RIO
D__
____
__
5-8
The
La
w o
f C
osi
ne
s a
nd
th
e P
yth
ag
ore
an
Th
eo
rem
Th
e la
w o
f co
sin
es b
ears
str
ong
sim
ilar
itie
s to
th
eP
yth
agor
ean
Th
eore
m.
Acc
ordi
ng
to t
he
Law
of
Cos
ines
, if t
wo
side
s of
a t
rian
gle
have
leng
ths
a an
db
and
if t
he a
ngle
bet
wee
n th
em h
as a
mea
sure
of x
,th
en t
he
len
gth
, y, o
f th
e th
ird
side
of
the
tria
ngl
eca
n b
e fo
un
d by
usi
ng
the
equ
atio
n
y2�
a2�
b2�
2ab
cos
(x°)
.
An
swer
th
e fo
llow
ing
qu
esti
ons
to c
lari
fy t
he
rela
tion
ship
bet
wee
n
the
Law
of
Cos
ines
an
d t
he
Pyt
hag
orea
n T
heo
rem
.
1.If
th
e va
lue
of x
beco
mes
less
an
d le
ss, w
hat
nu
mbe
r is
cos
(x°
)cl
ose
to?
12.
If t
he
valu
e of
xis
ver
y cl
ose
to z
ero
but
then
incr
ease
s, w
hat
hap
pen
s to
cos
(x°
) as
xap
proa
ches
90?
dec
reas
es, a
pp
roac
hes
03.
If x
equ
als
90, w
hat
is t
he
valu
e of
cos
(x°
)? W
hat
doe
s th
eeq
uat
ion
of
y2�
a2�
b2�
2ab
cos
(x°)
sim
plif
y to
if x
equ
als
90?
0, y
2�
a2
�b
2
4.W
hat
hap
pen
s to
th
e va
lue
of c
os (
x°)
as x
incr
ease
s be
yon
d 90
and
appr
oach
es 1
80?
dec
reas
es t
o –
15.
Con
side
r so
me
part
icu
lar
valu
es o
f a
and
b, s
ay 7
for
aan
d19
for
b.
Use
a g
raph
ing
calc
ula
tor
to g
raph
th
e eq
uat
ion
you
get
by s
olvi
ng
y2
�72
�19
2�
2(7)
(19)
cos
(x°
) fo
r y.
See
stu
den
ts’ g
rap
hs.
a.In
vie
w o
f the
geo
met
ry o
f the
sit
uati
on, w
hat
rang
e of
val
ues
shou
ld y
ou u
se f
or X
on
a g
raph
ing
calc
ula
tor?
Xm
in �
0; X
max
�18
0b
.D
ispl
ay t
he g
raph
and
use
the
TR
AC
E fu
ncti
on.
Wha
t do
the
max
imum
and
min
imum
val
ues
appe
ar t
o be
for
the
func
tion
?S
ee s
tud
ents
’ gra
phs
; Y
min
�12
, Ym
ax�
26c.
How
do
the
answ
ers
for
part
bre
late
to
the
len
gth
s 7
and
19?
Are
th
e m
axim
um
an
d m
inim
um
val
ues
fro
m p
art
bev
er
actu
ally
att
ain
ed in
th
e ge
omet
ric
situ
atio
n?
min
�(1
9�
7); m
ax �
(19
�7)
; no
© G
lenc
oe/M
cGra
w-H
ill20
3A
dva
nced
Mat
hem
atic
al C
once
pts
Pra
ctic
eN
AM
E__
____
____
____
____
____
____
___
DAT
E__
____
____
____
_ P
ER
IOD
____
____
Th
e L
aw
of
Co
sin
es
Sol
ve e
ach
tri
ang
le. R
oun
d t
o th
e n
eare
st t
enth
.
1.a
�20
, b�
12, c
�28
2.a
�10
, c�
8, B
�10
0�A
�38
.2�,
B�
21.8
�,
b�
13.8
, A�
45.5
�, C
�34
.5�
C�
120.
0�
3.c
�49
, b�
40, A
�53
�4.
a�
5, b
�7,
c�
10a
�40
.5, B
�52
.0�,
A
�27
.7�,
B�
40.5
�, C
�11
1.8�
C�
75.0
�
Fin
d t
he
area
of
each
tri
ang
le. R
oun
d t
o th
e n
eare
st t
enth
.
5.a
�5,
b�
12, c
�13
6.a
�11
, b�
13, c
�16
30.0
uni
ts2
71.0
uni
ts2
7.a
�14
,b�
9, c
�8
8.a
�8,
b�
7, c
�3
33.7
uni
ts2
10.4
uni
ts2
9.T
he
side
s of
a t
rian
gle
mea
sure
13.
4 ce
nti
met
ers,
18
.7 c
enti
met
ers,
an
d 26
.5 c
enti
met
ers.
Fin
d th
e m
easu
reof
th
e an
gle
wit
h t
he
leas
t m
easu
re.
abo
ut 2
8.3�
10.O
rien
teer
ing
Du
rin
g an
ori
ente
erin
g h
ike,
tw
o h
iker
s st
art
at p
oin
t A
and
hea
d in
a d
irec
tion
30�
wes
t of
sou
th
to p
oin
t B
.Th
ey h
ike
6 m
iles
fro
m p
oin
t A
to p
oin
t B
. Fro
m
poin
t B
,th
ey h
ike
to p
oin
t C
and
then
fro
m p
oin
t C
back
to
poin
t A
,wh
ich
is 8
mil
es d
irec
tly
nor
th o
f po
int
C.H
ow
man
y m
iles
did
th
ey h
ike
from
poi
nt
Bto
poi
nt
C?
4.1
mi
5-8
© Glencoe/McGraw-Hill A11 Advanced Mathematical Concepts
Page 205
1. B
2. D
3. A
4. A
5. C
6. B
7. D
8. A
9. C
10. D
11. C
12. A
13. B
Page 206
14. B
15. A
16. C
17. B
18. D
19. B
20. D
21. A
22. C
23. C
24. D
25. D
Bonus: B
Page 207
1. D
2. A
3. D
4. C
5. D
6. B
7. D
8. B
9. B
10. A
11. C
12. D
13. C
Page 208
14. A
15. B
16. A
17. A
18. A
19. C
20. C
21. B
22. B
23. B
24. C
25. D
Bonus: A
Chapter 5 Answer KeyForm 1A Form 1B
© Glencoe/McGraw-Hill A12 Advanced Mathematical Concepts
Chapter 5 Answer Key
Page 209
1. A
2. B
3. A
4. C
5. B
6. B
7. A
8. D
9. D
10. D
11. B
12. A
13. A
Page 210
14. C
15. A
16. B
17. A
18. B
19. B
20. C
21. C
22. B
23. D
24. D
25. C
Bonus: B
Page 211
1. 225° 38� 20.4
2. 23.274°
3. �864°
4.�180° and 180°
5. 22°
6. �41�16��
7. �52�
46��
8. �151�
9. � �12
�
10. 1
11. ��3�
12. ���31�3��
13. ��153�
Page 212
14. 179 feet
15. 48 feet
16. 150° and 330°
17. �45�
18. 68.2°
19. 17.6
20. 103.7 units2
21. two
22. 3.9
23. 12.0
24. 22.2°
25. 136.8 units2
Bonus: 1.054
Form 1C Form 2A
© Glencoe/McGraw-Hill A13 Advanced Mathematical Concepts
Chapter 5 Answer KeyForm 2B Form 2C
Page 213
1. 124° 37� 48
2. 48.538°
3. �450°
4. �90° and 270°
5. 50°
6. ��73�3��
7. �47�
8. ��43�3��
9. � �41�
10. 0
11. �2
12. ���44�1��
13. � �152�
Page 214
14. 186 feet
15. 135 feet
16. 210° and 330°
17. �1132�
18. 56.9°
19. 10.7
20. 164.9 units2
21. one
22. 9.9
23. 10.5
24. 129.8°
25. 154.7 units2
Bonus: �0.9487
Page 215
1. 25° 36� 00
2. 75.500°
3. 540°
4. 135°
5. 55°
6. ��96�5��
7. �4�65
6�5��
8. �49�
9. � �31�
10. 0
11. ��23��
12. �4�17
1�7��
13. � �153�
Page 216
14. 185 feet
15. 75 feet
16. 240° and 300°
17. �153�
18. 41.8°
19. 19.8
20. 120.7 units2
21. none
22. 19.8
23. 9.3
24. 117.3
25. 196.7 units2
Bonus: 1.000
© Glencoe/McGraw-Hill A14 Advanced Mathematical Concepts
Chapter 5 Answer KeyCHAPTER 5 SCORING RUBRIC
Level Specific Criteria
3 Superior • Shows thorough understanding of the concepts standard position, degree measure, quadrant, reference angle, and the six trigonometric functions of an angle.
• Computations are correct.• Uses appropriate strategies to solve problems.• Written explanations are exemplary.• Goes beyond requirements of some or all problems.
2 Satisfactory, • Shows understanding of the concepts standard position,with Minor degree measure, quadrant, reference angle, and the sixFlaws trigonometric functions of an angle.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Satisfies all requirements of problems.
1 Nearly • Shows understanding of most of the concepts standard Satisfactory, position, degree measure, quadrant, reference angle, with Serious and the six trigonometric functions of an angle.Flaws • May not use appropriate strategies to solve problems.
• Computations are mostly correct.• Written explanations are satisfactory.• Satisfies most requirements of problems.
0 Unsatisfactory • Shows little or no understanding of the concepts standard position, degree measure, quadrant, reference angle, and the six trigonometric functions of an angle.
• May not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are not satisfactory.• Does not satisfy requirements of problems.
© Glencoe/McGraw-Hill A15 Advanced Mathematical Concepts
Page 217
1a. 210°, 570°, 930°
1b. The cosine is �xr
� � �2�
�33�
�, or
���23��.
1c. first quadrant: 30°, second quadrant: 150°, fourth quadrant: 330°
1d. Sample answers:(�3, 4); sin A � �
54�,
cos A � � �35
�, tan A � � �43
�,
csc A � �54
�, sec A � � �53
�,
cot A � � �43�
2a. The length of the missing sideto the east is given by
�s1in5
4ft0.°
� � �sin
x60°� , or 20.2 feet.
The length of the missing sidearound the fountain is given by �1
6� 20�, or 10.5 feet.
The total length isapproximately 140.7 feet.
2b. Answers will vary but mightinclude issues such as thelength of fence required versusthe increase in park size, access and/orproximity to roads,maintenance and/orenhancement of the fountain, and so on.
Chapter 5 Answer KeyOpen-Ended Assessment
© Glencoe/McGraw-Hill A16 Advanced Mathematical Concepts
Mid-Chapter TestPage 218
1. 65° 46� 55.2
2. 250°; III
3. �2�11
1�0��
4. �2�91�0��
5. � �31�
6. 0
7. ���23��
8. ��5�
9. 9.2
10. 11.0
Quiz APage 219
1. 47° 16� 59
2. 122.720°
3. 810°
4. 120° and �240°
5. 37°6. �3�
343�4��
7. �53�
8. ��53�4��
9. � �23�
10. 2
Quiz BPage 219
1. �1
2. undefined3. ���
23��
4. �15. ��
44�1��
6. ��153�
7. 6.6
8. 9.8
9. 83.9 feet
10. 54.5 feet
Quiz CPage 220
1. 210° and 330°
2. �152�
3. 35.7°
4. 48.8
5. 78.7 units2
Quiz DPage 220
1. none
2. 70.6°
3. 9.1
4. 60.1°
5. 498.0 units2
Chapter 5 Answer Key
© Glencoe/McGraw-Hill A17 Advanced Mathematical Concepts
Page 221
1. D
2. D
3. A
4. C
5. E
6. E
7. B
8. D
9. D
10. B
Page 222
11. D
12. A
13. E
14. C
15. A
16. B
17. B
18. A
19. 24
20. 361
Page 223
1. �2x
1� 4�
2. perpendicular
3.
4. (3, �1)
5. � �
6.
7. y-axisreflected over x-axis; translated left 2 units
8. and down 5 units
9. y � �x �2
6� ; yes
10. 3 � �3�
11. �29
12. �1
13. 15.4
14. 36.9°
38�15
�3437
Chapter 5 Answer KeySAT/ACT Practice Cumulative Review
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