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Complete Unit 6
Package
HighSchoolMathTeachers.com©2020
Table of Contents
Unit 6 Pacing Chart -------------------------------------------------------------------------------------------- 1
Geometry Unit 6 Skills List ---------------------------------------------------------------------------------------- 5
Unit 6 Lesson Plans -------------------------------------------------------------------------------------------- 6
Day 86 Bellringer -------------------------------------------------------------------------------------------- 42
Day 86 Activity -------------------------------------------------------------------------------------------- 44
Day 86 Practice -------------------------------------------------------------------------------------------- 47
Day 86 Exit Slip -------------------------------------------------------------------------------------------- 53
Day 87 Bellringer -------------------------------------------------------------------------------------------- 55
Day 87 Activity -------------------------------------------------------------------------------------------- 57
Day 87 Practice -------------------------------------------------------------------------------------------- 59
Day 87 Exit Slip -------------------------------------------------------------------------------------------- 62
Day 88 Bellringer -------------------------------------------------------------------------------------------- 64
Day 88 Activity -------------------------------------------------------------------------------------------- 66
Day 88 Practice -------------------------------------------------------------------------------------------- 68
Day 88 Exit Slip -------------------------------------------------------------------------------------------- 72
Day 89 Bellringer -------------------------------------------------------------------------------------------- 74
Day 89 Activity -------------------------------------------------------------------------------------------- 76
Day 89 Practice -------------------------------------------------------------------------------------------- 79
Day 89 Exit Slip -------------------------------------------------------------------------------------------- 84
Week 18 Assessment -------------------------------------------------------------------------------------------- 86
Day 91 Bellringer -------------------------------------------------------------------------------------------- 93
Day 91 Activity -------------------------------------------------------------------------------------------- 95
Day 91 Practice -------------------------------------------------------------------------------------------- 97
Day 91 Exit Slip -------------------------------------------------------------------------------------------- 101
Day 92 Bellringer -------------------------------------------------------------------------------------------- 103
Day 92 Activity -------------------------------------------------------------------------------------------- 105
Day 92 Practice -------------------------------------------------------------------------------------------- 108
Day 92 Exit Slip -------------------------------------------------------------------------------------------- 111
Day 93 Bellringer -------------------------------------------------------------------------------------------- 113
Day 93 Activity -------------------------------------------------------------------------------------------- 115
Day 93 Practice -------------------------------------------------------------------------------------------- 117
Day 93 Exit Slip -------------------------------------------------------------------------------------------- 122
Day 94 Bellringer -------------------------------------------------------------------------------------------- 124
Day 94 Activity -------------------------------------------------------------------------------------------- 126
Day 94 Practice -------------------------------------------------------------------------------------------- 129
Day 94 Exit Slip -------------------------------------------------------------------------------------------- 133
Week 19 Assessment -------------------------------------------------------------------------------------------- 135
Day 96 Bellringer -------------------------------------------------------------------------------------------- 142
Day 96 Activity -------------------------------------------------------------------------------------------- 144
Day 96 Practice -------------------------------------------------------------------------------------------- 146
Day 96 Exit Slip -------------------------------------------------------------------------------------------- 149
Day 97 Bellringer -------------------------------------------------------------------------------------------- 151
Day 97 Activity -------------------------------------------------------------------------------------------- 153
Day 97 Practice -------------------------------------------------------------------------------------------- 155
Day 97 Exit Slip -------------------------------------------------------------------------------------------- 161
Day 98 Bellringer -------------------------------------------------------------------------------------------- 163
Day 98 Activity -------------------------------------------------------------------------------------------- 165
Day 98 Practice -------------------------------------------------------------------------------------------- 167
Day 98 Exit Slip -------------------------------------------------------------------------------------------- 170
Day 99 Bellringer -------------------------------------------------------------------------------------------- 172
Day 99 Activity -------------------------------------------------------------------------------------------- 175
Day 99 Practice -------------------------------------------------------------------------------------------- 178
Day 99 Exit Slip -------------------------------------------------------------------------------------------- 183
Week 20 Assessment -------------------------------------------------------------------------------------------- 185
Day 101 Bellringer -------------------------------------------------------------------------------------------- 190
Day 101 Activity -------------------------------------------------------------------------------------------- 192
Day 101 Practice -------------------------------------------------------------------------------------------- 194
Day 101 Exit Slip -------------------------------------------------------------------------------------------- 198
Day 102 Bellringer -------------------------------------------------------------------------------------------- 200
Day 102 Activity -------------------------------------------------------------------------------------------- 202
Day 102 Practice -------------------------------------------------------------------------------------------- 205
Day 102 Exit Slip -------------------------------------------------------------------------------------------- 209
Day 103 Bellringer -------------------------------------------------------------------------------------------- 211
Day 103 Activity -------------------------------------------------------------------------------------------- 213
Day 103 Practice -------------------------------------------------------------------------------------------- 215
Day 103 Exit Slip -------------------------------------------------------------------------------------------- 218
Day 104 Bellringer -------------------------------------------------------------------------------------------- 221
Day 104 Activity -------------------------------------------------------------------------------------------- 223
Day 104 Practice -------------------------------------------------------------------------------------------- 225
Day 104 Exit Slip -------------------------------------------------------------------------------------------- 229
Week 21 Assessment -------------------------------------------------------------------------------------------- 231
Unit 6 Test -------------------------------------------------------------------------------------------- 236
Unit 6 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 1
Unit Week Day CCSS Standards Objective I Can Statements
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 86
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Identify opposite, adjacent and hypotenuse of right
triangles. Define trigonometric ratios.
I can Identify opposite, adjacent and hypotenuse of
right triangles I can define trigonometric
ratios.
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 87
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Find trigonometric ratios of angles
I can find trigonometric ratios of angles
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 88
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Define trigonometric ratios of compliments.
I can define trigonometric ratios of compliments.
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 89
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Use similarity to find the trigonometric ratios of triangles with common
angles.
I can use similarity to find the trigonometric ratios of
triangles with common angles.
Unit 6 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 2
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 90 Assessment Assessment Assessment
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 91
CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine
and cosine of complementary angles.
Explain the relationship between sine and cosine of
complementary angles
I can explain the relationship between sine
and cosine of complementary angles
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 92
CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine
and cosine of complementary angles.
Use the relationship between the sine and cosine of complementary angles to
solve geometric problems
I can use the relationship between the sine and cosine of complementary angles to
solve geometric problems
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 93
CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.*
Use trigonometric ratios to solve a triangle
I can use trigonometric ratios to solve a triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 94
CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.*
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
word problems
I can use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in word problems
Unit 6 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 3
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 95 Assessment Assessment Assessment
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 96
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Find the trigonometric ratios of 30-60-90 right triangle
I can find the trigonometric ratios of 30-60-90 right
triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 97
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Solve 30-60-90 right triangle I can solve 30-60-90 right
triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 98
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Find the trigonometric ratios of 45-45-90 right triangle
I can find the trigonometric ratios of 45-45-90 right
triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 99
CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
Solve 45-45-90 right triangle I can solve 45-45-90 right
triangle
Unit 6 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 4
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 100 Assessment Assessment Assessment
Geometry Unit 6 Skills List Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 5
Geometry Unit 6 Skills List
Number Unit CCSS Skill
24 6 HSG.SRT.C.6 Define trigonometric ratios for acute angles
25 6 HSG.SRT.C.7 Explain the relationship between the sine and cosine
of complementary angles
26 6 HSG.SRT.C.7 Use the relationship between the sine and cosine of
complementary angles
27 6 HSG.SRT.C.8 Solve right triangles in applied problems
28 6 HSG.SRT.D.9 Derive the formula A = 1/2ab sin(C) for the area of a
triangle
29 6 HSG.SRT.D.10 Prove the Laws of Sine’s and Cosines
30 6 HSG.SRT.D.10 Use the Laws of Sine’s and Cosines to solve problems
31 6 HSG.SRT.D.11
Apply the Law of Sine’s and the Law of Cosines to find
unknown measurements in right and non-right
triangles
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 6
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 18 – Indirect Measurements
Day: 86
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively
Objective: Identify opposite, adjacent and hypotenuse of right triangles. Define trigonometric ratios.
I can statement: I can Identify opposite, adjacent and hypotenuse of right triangles I can define trigonometric ratios.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will identify the opposite side, the adjacent side and the hypotenuse of angles in a right triangle 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 86 Day 86 Activities Day 86 Practice Day 86 Presentation Day 86 Exit Slip
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 7
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 8
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 18 – Indirect Measurements
Day: 87
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively
Objective: Find trigonometric ratios of angles
I can statement: I can find trigonometric ratios of angles
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw a right angle and verify the trigonometric ratios 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 87 Day 87 Activities Day 87 Practice Day 87 Presentation Day 87 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 9
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 10
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 18 – Indirect Measurements
Day: 88
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively
Objective: Define trigonometric ratios of compliments.
I can statement: I can define trigonometric ratios of compliments.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least four to compare trigonometric ratios of two complementary angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 88 Day 88 Activities Day 88 Practice Day 88 Presentation Day 88 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 11
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 12
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 18 – Indirect Measurements
Day: 89
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Objective: Use similarity to find the trigonometric ratios of triangles with common angles.
I can statement: I can use similarity to find the trigonometric ratios of triangles with common angles.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw similar triangles from a rectangle and find the trigonometric ratios of a common angle. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 89 Day 89 Activities Day 89 Practice Day 89 Presentation Day 89 Exit Slip
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 13
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 14
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 18 – Indirect Measurements
Day: 90
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 15
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 19 – Trigonometric Ratios
Day: 91
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Objective: Explain the relationship between sine and cosine of complementary angles
I can statement: I can explain the relationship between sine and cosine of complementary angles
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw a right angle and verify the equality of sine and cosine of complementary angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 91 Day 91 Activities Day 91 Practice Day 91 Presentation Day 91 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 16
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 17
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 19 – Trigonometric Ratios
Day: 92
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Use the relationship between the sine and cosine of complementary angles to solve geometric problems
I can statement: I can use the relationship between the sine and cosine of complementary angles to solve geometric problems
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 92 Day 92 Activities Day 92 Practice Day 92 Presentation Day 92 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 18
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 19
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 19 – Trigonometric Ratios
Day: 93
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
Objective: Use trigonometric ratios to solve a triangle
I can statement: I can use trigonometric ratios to solve a triangle
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 93 Day 93 Activities Day 93 Practice Day 93 Presentation Day 93 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 20
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 21
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 19 – Trigonometric Ratios
Day: 94
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
Objective: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in word problems
I can statement: I can use trigonometric ratios and the Pythagorean Theorem to solve right triangles in word problems
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 94 Day 94 Activities Day 94 Practice Day 94 Presentation Day 94 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 22
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 23
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 19 – Trigonometric Ratios
Day: 95
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 24
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 20 – Special Right Triangles
Day: 96
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Find the trigonometric ratios of 30-60-90 right triangle
I can statement: I can find the trigonometric ratios of 30-60-90 right triangle
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 96 Day 96 Activities Day 96 Practice Day 96 Presentation Day 96 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 25
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 26
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 20 – Special Right Triangles
Day: 97
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP1. Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Solve 30-60-90 right triangle
I can statement: I can solve 30-60-90 right triangle
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 97 Day 97 Activities Day 97 Practice Day 97 Presentation Day 97 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 27
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 28
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 20 – Special Right Triangles
Day: 98
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP1. Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Find the trigonometric ratios of 45-45-90 right triangle
I can statement: I can find the trigonometric ratios of 45-45-90 right triangle
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 98 Day 98 Activities Day 98 Practice Day 98 Presentation Day 98 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 29
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 30
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 20 – Special Right Triangles
Day: 99
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical Practice: CCSS.MATH.PRACTICE.MP1. Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Solve 45-45-90 right triangle
I can statement: I can solve 45-45-90 right triangle
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 99 Day 99 Activities Day 99 Practice Day 99 Presentation Day 99 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 31
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 32
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 20 – Special Right Triangles
Day: 100
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 33
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 21 – Modeling with Right Triangles
Day: 101
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively
Objective: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
I can statement: I can derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 101 Day 101 Activities Day 101 Practice Day 101 Presentation Day 101 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 34
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 35
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 21 – Modeling with Right Triangles
Day: 102
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively
Objective: Derive and apply sine rules
I can statement: I can derive and apply sine rules
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 102 Day 102 Activities Day 102 Practice Day 102 Presentation Day 102 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 36
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 37
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 21 – Modeling with Right Triangles
Day: 103
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively
Objective: Derive and apply cosine rules
I can statement: I can derive and apply cosine rules
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 103 Day 103 Activities Day 103 Practice Day 103 Presentation Day 103 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 38
Reflection:
Extra/Additional Resources:
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 39
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 21 – Modeling with Right Triangles
Day: 104
Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
I can statement: I Understand and can apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 104 Day 104 Activities Day 104 Practice Day 104 Presentation Day 104 Exit Slip
Unit 6 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 40
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Day 86 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 41
Unit: Unit 6 Right Triangle Relationships and Trigonometry
Course: Geometry
Topic: Week 21 – Modeling with Right Triangles
Day: 105
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Day 86 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 42
Use right ΔPQR (not drawn to scale) to answer the questions below.
1. Find the length QR.
2. Find the size of ∠QPR
3. Express the following length ratios in their simplest forms:
(a) PQ
QR
(b) PQ
PR
(c) QR
PR
P
Q R
14 in.
50 in.
16.3°
Day 86 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 43
Answer keys
Day 86:
1. 48 in.
2. 73.7°
3. (a) 7
24
(b) 7
25
(c) 24
25
Day 86 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 44
1. Measure ∠X and fill its measure in the table provided.
2. Measure the measure the length of the hypotenuse and fill the length in the table provided below.
3. Measure the length of the side adjacent to ∠X and fill its length in the table under the column
labeled; length of the adjacent side. Note the position of the adjacent side with respect to ∠X.
X
Y Z
Day 86 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 45
4. Measure the length of the side opposite to ∠X and fill in the table under the column labeled; length of
opposite side. Note the position of the opposite side with respect to ∠X.
5. Now use the measurements to determine the ratios of the indicated sides correct to two decimal
places, then fill in the three columns of the table.
6. Similarly, measure ∠Z and follow the steps 1-5 above to complete the second row of the table.
Table 1
Angle Angle measure
Length of hypotenuse
Length of adjacent side
Length of opposite side
Opposite side
Hypotenuse
Adjacent side
Hypotenuse
Opposite side
Adjacent side
∠𝑋
∠𝑍
Day 86 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 46
In this activity students will work in groups of three to identify the opposite side, the adjacent side and
the hypotenuse of angles in a right triangle and to determine the ratios of these sides. Each of the
groups will be provided with a copy of ∆XYZ, a copy of table 1, a protractor and a ruler calibrated in
inches.
Answer keys Day 86:
1. Accuracy to be emphasized
2. Accuracy to be emphasized
3. Students should note that XY is adjacent to ∠X
4. Students should note that YZ is opposite to ∠X
5. The ratio 1.33 is written correct to two decimal places
6. Students should repeat the process, noting the adjacent and opposite sides in relation to ∠Z as they
did for ∠X
Table 1
Angle Angle measure
Length of hypotenuse
Length of adjacent side
Length of opposite side
Opposite side
Hypotenuse
Adjacent side
Hypotenuse
Opposite side
Adjacent side
∠𝑋 37° 5 in 4 in. 3 in. 0.6 0.8 0.75
∠𝑍 53° 5 in. 3 in. 4 in. 0.8 0.6 1.33
Day 86 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 47
Use right ∆𝐗𝐘𝐙 to answer question 1- 6 below.
Identify the following sides in relation to 𝛾.
1. The hypotenuse
2. The opposite side
3. The adjacent side
Use the sides of ∆XYZ to define the following trigonometric ratios, using 𝛾 as the reference angle:
4. tan 𝛾
5. cos 𝛾
6. sin 𝛾
X
Y Z
𝛾
Day 86 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 48
Use right 𝚫𝐉𝐊𝐋 below to answer questions 7-12.
Name the following sides with reference to 𝜙.
7. opposite side
8. Adjacent side
9. Hypotenuse
Name the following sides with reference to 𝜏.
10. opposite side
11. Adjacent side
12. Hypotenuse
J
K
L
𝜙
𝜏
Day 86 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 49
13. Sketch ΔPQR such that 𝜆 is the reference angle, PR is the opposite side, PQ is the adjacent side and
QR is the hypotenuse.
Study the figure below and use it to answer question 14 and 15.
If a person standing at point T glances up at the top of the building:
14. What name will be given to the side representing the distance from the person to the foot of the
building in relation to ΔTVS and ∠T?
15. What name will be given to the side representing the height of the building in relation to ΔTVS and
∠T?
16. Identify the hypotenuse from the figure above.
T
S
V
Bu
ildin
g
Day 86 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 50
17. Show on the right ΔFGH the location of acute angle 𝛼 given that FG is the adjacent side.
The figure below shows the dimensions of a triangular pond represented as right 𝚫𝐁𝐂𝐃.
Use it to answer questions 18-20. All the dimensions are in feet.
State the lengths of the following sides with reference to ∠D:
18. The opposite side
19. The hypotenuse.
20. Calculate the length of the adjacent side.
F
H
G
B
D
C
841
840
Day 86 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 51
Answer keys
Day 86:
1. XZ
2. XY
3. YZ
4. 𝑋𝑌
𝑌𝑍
5. 𝑌𝑍
𝑋𝑍
6. 𝑋𝑌
𝑋𝑍
7. KL
8. JK
9. JL
10. JK
11. KL
12. JL
13.
14. Adjacent side
15. opposite side
16. TS
P
R
Q
𝜆
Day 86 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 52
17.
18. 840 ft.
19. 841 ft.
20. 41 ft.
F
H
G
𝛼
Day 86 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 53
In ∆KLM identify the hypotenuse, the adjacent side and the opposite side for the marked acute angle 𝛼.
𝛼
K L
M
Day 86 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 54
Answer keys Day 86:
KM is the hypotenuse
LM is the adjacent side
KL is the opposite side
Day 87 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 55
Use the following diagram to answer the following questions
Identify the following from 1 - 3.
1. Adjacent side to 𝜏 and 𝛼.
2. Opposite side to 𝜏 and 𝛼.
3. Hypotenuse to 𝜏 and 𝛼.
4. Write the expressions for tan 𝜏 and sin 𝛼
5. Write the expressions for cos 𝛼 and sec 𝜏.
M N
T
𝜏
𝛼
Day 87 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 56
Answer Keys
Day 87:
1. Adjacent side to 𝜏, 𝑀𝑇̅̅̅̅̅
Adjacent side to 𝛼 𝑀𝑁̅̅ ̅̅ ̅
2. Opposite side to 𝜏, 𝑀𝑁̅̅ ̅̅ ̅
Opposite side to 𝛼 𝑀𝑇̅̅̅̅̅
3. Hypotenuse side to 𝑁𝑇̅̅ ̅̅
4. tan 𝜏 =𝑀𝑁̅̅ ̅̅ ̅
𝑀𝑇̅̅ ̅̅̅
sin 𝛼 =𝑀𝑇̅̅̅̅̅
𝑁𝑇̅̅ ̅̅
5. cos 𝛼 =𝑀𝑁̅̅ ̅̅ ̅
𝑁𝑇̅̅ ̅̅
sec 𝜏 =𝑁𝑇̅̅ ̅̅
𝑀𝑇̅̅̅̅̅
Day 87 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 57
1. Draw any right angle triangle and label it as shown below.
2. Measure segments 𝐷𝐸̅̅ ̅̅ , 𝐸𝐹̅̅ ̅̅ and 𝐹𝐷̅̅ ̅̅ .
3. Measure the following angles ∠𝐷 and ∠𝐹
4. Use measurements in 2 above to find sine, cosine, and tangent of ∠𝐷 and ∠𝐹.
5. Use measurements in 3 above to find sine, cosine, and tangent of ∠𝐷 and ∠𝐹.
6. Compare the similar ratios of the same angles in 4 and 5 above.
D E
F
Day 87 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 58
In this activity, students will draw a right angle and verify the trigonometric ratios. Each group will be
composed of at least 3 students and will require a protractor, a ruler, a pencil and a plane paper.
Answer Keys
Day 87:
1. No response
2. Different responses but must satisfy the Pythagorean Theorem.
3. Different responses but must add up to 90°.
4 - 5. Different responses
6. Similar ratios of the same angles
Day 87 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 59
Use the following information to answer questions 1 – 11
Find the following ratios
1. cos𝛼
2. sin 𝛼
3. tan 𝛼
4. cos𝜃
5. sin 𝜃
6. tan 𝜃
7. sec 𝜃
8. cot 𝜃
9. cot 𝛼
10. csc 𝜃
11. sec 𝛼
G H
J
𝛼
𝜃
6 in
16 in
17.08 in
Day 87 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 60
Use the following information to answer questions 12 - 18
Find the following trigonometric ratios
12. tan ∠𝐻
13. cos 𝛼
14. sin 𝛼
15. tan 𝛼
16. sin ∠𝐻
17. cot ∠𝐻
18. sec ∠𝐻
19. Find the tangent and sine of 90°
20. Find the tangent and sine of 80°
G H
J
𝛼
48°
Day 87 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 61
Answer keys
Day 87:
1. 0.3513
2. 0.9368
3. 2.667
4. 0.9368
5. 0.3513
6. 0.375
7. 1.068
8. 2.667
9. 0.375
10. 2.847
11. 2.847
12. 1.111
13. 0.7431
14. 0.6691
15. 0.9004
16. 0.7431
17. 0.9004
18. 1.494
19. tan 90° 𝑖𝑠 𝑛𝑜𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑
sin 90° = 1
20. tan 80° = 5.671
sin 80° = 0.9848
Day 87 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 62
The opposite and adjacent side of an angle in a right triangle is 12 in and 9 in respectively. Find the
cosine, tangent and cosecant of the angle.
Day 87 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 63
Answer Keys
Day 87
Let the angle be 𝑥
cos 𝑥 = 0.6
tan 𝑥 = 1.333
csc 𝑥 = 1.25
Day 88 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 64
1. Find the complements of the following angles.
(a) 11°
(b) 89°
(c) 𝜃
2. In right ∆PQR below ∠QPR = 𝛼. Use it to answer the questions that follow.
(a) Find the measure of ∠PRQ in terms of 𝛼.
(b) Identify the side adjacent to ∠PRQ
(c) Identify the side opposite to ∠PRQ
R
Q P
𝛼
Day 88 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 65
Answer keys
Day 88:
1. (a) 79°
(b) 1°
(c) 90° − 𝜃
2. (a) 90° − 𝛼
(b) QR
(c) PQ
Day 88 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 66
1. Measure ∠𝐹 and write down its measure.
2. Measure ∠𝐻 and write down its measure.
3. Find the sum of ∠𝐹 and ∠𝐻. What is the name given to such a pair of angles?
4. Express the sine, cosine and tangent of ∠𝐹 in terms of 𝑓, 𝑔 and ℎ where applicable.
5. Express the sine, cosine and tangent of ∠𝐻 in terms of 𝑓, 𝑔 and ℎ where applicable.
6. Compare the expressions for the sines, cosines and tangents of the two angles. State whether the
expressions are similar or different for each trigonometric ratio of the each of the two angles.
F
G H
𝑔 ℎ
𝑓
Day 88 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 67
In this activity, students will work in groups of four to compare trigonometric ratios of two
complementary angles. The students in the groups will be equipped with a protractor, and a copy of
right ∆FGH labeled such that ∠𝐺 is the right angle, ∠𝐹 = 30° and ∠𝐻 = 60°. The sides should be
labelled as shown.
Answer keys
Day 88:
1. ∠𝐹 = 30°
2. ∠𝐻 = 60°
3. The sum is 90°; Complementary angles
4. sin 𝐹 =𝑓
𝑔
cos 𝐹 =ℎ
𝑔
tan 𝐹 =𝑓
ℎ
5. sin 𝐻 =ℎ
𝑔
cos 𝐻 =𝑓
𝑔
tan 𝐻 =ℎ
𝑓
6. The expressions are different for each trigonometric ratio of each angle.
Day 88 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 68
Use right ∆𝐉𝐊𝐋 below to answer questions 1-8.
1. Find the sum 𝛼 + 𝛽.
2. What is the name was given to the pair of angles 𝛼 and 𝛽 from your sum in question 1 above?
Express the following trigonometric ratios of 𝜶 in terms of 𝒋, 𝒌 and 𝒍 where applicable.
3. sin 𝛼
4. cos 𝛼
5. tan 𝛼
Similarly, express the following trigonometric ratios of 𝜷 in terms of 𝒋, 𝒌 and 𝒍 where applicable.
6. sin 𝛽
7. cos 𝛽
8. tan 𝛽
J
K L
𝑘
𝑙
𝑗
𝛽
𝛼
Day 88 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 69
Use right ∆𝐑𝐒𝐓 below to answer questions 9-16.
9. Write ∠𝑇 in terms of 𝜏
10. What is the sum of ∠𝑅 and ∠𝑇?
Express the following trigonometric ratios of ∠𝑅 in terms of 𝑟, 𝑠 and 𝑡 where applicable.
11. sin 𝑅
12. cos 𝑅
13. tan 𝑅
Express the following trigonometric ratios of ∠𝑇 in terms of 𝑟, 𝑠 and 𝑡 where applicable.
14. sin 𝑇
15. cos 𝑇
16. tan 𝑇
R
S T
𝑠
𝑡
𝑟
𝜏
Day 88 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 70
In right ∆𝐌𝐍𝐏 below ∠𝑷 = 𝟗𝟎° − 𝜽. Use it to answer questions 17-20.
17. Write ∠𝑀 in terms of 𝜃.
18. Write an expression as a ratio in terms of 𝑚, 𝑛 and 𝑝 where applicable to show the sine of 90° − 𝜃
19. Write an expression as a ratio in terms of 𝑚, 𝑛 and 𝑝 where applicable to show the cosine of 90° −
𝜃
20. Write an expression in as a ratio in terms of 𝑚, 𝑛 and 𝑝 where applicable to show the tangent of
90° − 𝜃
M
N P
𝑛
𝑝
𝑚
90° − 𝜃
Day 88 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 71
Answer keys
Day 88:
1. 90°
2. 𝛼 and 𝛽 are complements to each other/
they are complementary angles
3. sin 𝛼 =𝑙
𝑘
4. cos 𝛼 =𝑗
𝑘
5. tan 𝛼 =𝑙
𝑗
6. sin 𝛽 =𝑗
𝑘
7. cos 𝛽 =𝑙
𝑘
8. tan 𝛽 =𝑗
𝑙
9. 90° − 𝜏
10. 90°
11. sin 𝑅 =𝑟
𝑠
12. cos 𝑅 =𝑡
𝑠
13. tan 𝑅 =𝑟
𝑡
14. sin 𝑇 =𝑡
𝑠
15. sin 𝑇 =𝑟
𝑠
16. tan 𝑇 =𝑡
𝑟
17. 𝜃
18. sin(90° − 𝜃) =𝑝
𝑛
19. cos(90° − 𝜃) =𝑚
𝑛
20. tan(90° − 𝜃) =𝑝
𝑚
Day 88 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 72
Use right ∆KLM to answer the questions that follow.
(a) Find the sum 𝛼 + (90° − 𝛼).
(b) Express the sine of (90° − 𝛼) in terms of 𝑘 and 𝑙.
(c) Express the cosine of (90° − 𝛼) in terms of 𝑚 and 𝑙.
K
L M
𝑙
𝑚
𝑘
90° − 𝛼
𝛼
Day 88 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 73
Answer keys
Day 88:
(a) 90°
(b) 𝑘
𝑙
(c) 𝑚
𝑙
Day 89 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 74
1.Use the figure below to answer the questions that follow.
a) Calculate sin 𝜃
b) Calculate cos 𝜃
c) Calculate tan 𝜃
d) Calculate cos 𝛼
2. Which angle is shared by ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐶?
A B
C
D E
𝛼
𝜃
6 𝑖𝑛 3 𝑖𝑛
5.2 𝑖𝑛
Day 89 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 75
Answer Key Day 89:
1. a) 0.5
b) 0.867
c) 0.577
d) 0.5
2. ∠𝐶
Day 89 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 76
1. Construct a rectangle measuring 3 𝑖𝑛 by 4 𝑖𝑛 on a plane paper and label it ABCD such that the longer
sides are AB and CD as shown.
2. Measure 1 𝑖𝑛 from A along side AD and label it E.
3. Measure 1 𝑖𝑛 from A along side BC and label it F.
4. Draw a diagonal to join A and C and label its intersection point with line EF as G.
5. Which angle is common in ∆𝐴𝐷𝐶 and ∆𝐴𝐷𝐺?
6. Measure the lengths of sides in the first row of the table below and record them in the second row.
AD DC AC AE EG GA
A B
D C
Day 89 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 77
7. Find the trigonometric ratios of ∠𝐶𝐴𝐷 and ∠𝐺𝐴𝐸 and record your results in the following table. Write
your answer in one decimal place.
∠𝐶𝐴𝐷 ∠𝐺𝐴𝐸
sin
cos
tan
Day 89 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 78
In this activity, students will draw similar triangles from a rectangle and find the trigonometric ratios of a
common angle. Students will work in groups of at least three and each group is required to have a ruler,
a protractor a pencil and a plain paper.
Answer Keys Day 89:
1-4. No response
5. ∠𝐴
6.
AD DC AC AE EG GA
𝟑 𝒊𝒏 4 𝑖𝑛 5 𝑖𝑛 1 𝑖𝑛 1.3 𝑖𝑛 1.7 𝑖𝑛
7.
∠𝐶𝐴𝐷 ∠𝐺𝐴𝐸
sin 0.8 0.8
cos 0.6 0.6
tan 1.3 1.7
Day 89 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 79
Use the figure below to answer questions 1-6.
Leave your answer in fraction form.
.
1. Calculate the cosine of ∠𝑆𝑇𝑈.
2. Calculate the cosine of ∠𝑀𝑇𝑁.
3. Calculate the sine of ∠𝑆𝑇𝑈.
4. Calculate the sine of ∠𝑀𝑇𝑁
5. Calculate the tangent of ∠𝑆𝑇𝑈
6. Calculate the tangent of ∠𝑀𝑇𝑁
S M T
U
N
60 𝑖𝑛 120 𝑖𝑛
33 𝑖𝑛
61 𝑖𝑛
122 𝑖𝑛
22 𝑖𝑛
Day 89 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 80
Use the diagram below to answer questions 7-12.
7. Calculate the sine of ∠𝐴𝐿𝐵.
8. Calculate the sine of ∠𝐽𝐿𝐾.
9. Calculate the cosine of ∠𝐴𝐿𝐵.
10. Calculate the cosine of ∠𝐽𝐿𝐾.
11. Calculate the tangent of ∠𝐴𝐿𝐵.
12. Calculate the sine of ∠𝐽𝐿𝐾.
J
K
L
A
B
8 𝑖𝑛 12 𝑖𝑛
8 𝑖𝑛
6 𝑖𝑛
10 𝑖𝑛
10 𝑖𝑛
Day 89 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 81
Use the diagram below to answer questions 13-18
13. Calculate the sine of ∠𝐽𝐶𝐾.
14. Calculate the sine of ∠𝐴𝐶𝐵.
15. Calculate the cosine of ∠𝐽𝐶𝐾.
16. Calculate the cosine of ∠𝐴𝐶𝐵.
17. Calculate the tangent of ∠𝐴𝐶𝐵.
18. Calculate the tangent of ∠𝐽𝐶𝐾
A
B
C
J
K
20 𝑖𝑛 63 𝑖𝑛
40 𝑖𝑛
58 𝑖𝑛
29 𝑖𝑛
21 𝑖𝑛
Day 89 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 82
Use the diagram below to answer questions 19 and 20
19. Calculate the cosine of ∠𝑇𝑅𝑈.
20. Calculate the cosine of ∠𝑄𝑅𝑆.
Q R
S
T
U
5 𝑖𝑛 5 𝑖𝑛
24 𝑖𝑛 13 𝑖𝑛
13 𝑖𝑛
Day 89 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 83
Answer Keys
Day 89:
1. 60
61
2. 60
61
3. 11
61
4. 11
61
5. 11
60
6. 11
60
7. 3
5
8. 3
5
9. 4
5
10. 4
5
11. 3
4
12. 3
4
13. 21
29
14. 21
29
15. 20
29
16. 20
29
17. 21
20
18. 21
20
19. 5
13
20. 5
13
Day 89 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 84
In the diagram below, 𝐶𝑇 = 3 𝑖𝑛 and 𝑆𝑇 = 3.6 𝑖𝑛.
Calculate the tangent of ∠𝐴𝐶𝐵
A B
C
S T
Day 89 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 85
Answer Keys Day 89:
1. 1.2
86
High School Math Teachers
Geometry
Weekly Assessment Package
Week 18
©2020HighSchoolMathTeachers
87
Week 18
Weekly Assessment
88
Week #18
1. The following images are similar.
a). Find the length of NL and NM b). What would the distance around NL?
2. a).Identify the reason that makes the two triangles similar.
b). Then find the value of the third angle
2 in 9 in
6 in
6.5 in
L
M
N
20°
20°
115°
115°
89
3. Use the diagram below to answer the
questions
a). Identify the opposite and adjacent sides to 𝛼
b). Express the sine and tangent of 𝛼 in terms of the sides of the triangle
4. Use postulates of congruence and similarity to
show that triangle ABC and ACD are congruent if
ABCD is a rectangle.
5. Find the trigonometric ratios of 30°, 25° and
68° 6. Given that sin 𝜃 =
1
3
a). Find 𝑐𝑜𝑠 𝜃 and tan 𝜃 (give the exact answer)
b). Find sin(90° − 𝜃)
N M
P
𝛼
A B
C D
90
Week 18 - KEYS
Weekly Assessments
91
Week #18 KEY 1. The following images are similar.
a). Find the length of NL and NM 27 in b). What would the distance around NL? 29.25 in
2. a).Identify the reason that makes the two triangles similar.
AA criterion b). Then find the value of the third angle 45°
2 in 9 in
6 in
6.5 in
L
M
N
20°
20°
115°
115°
92
3. Use the diagram below to answer the
questions
a). Identify the opposite and adjacent sides to 𝛼 Opposite side is NM Adjacent side is PN b). Express the sine and tangent of 𝛼 in terms of the sides of the triangle
sin 𝛼 =𝑁𝑀
𝑃𝑀; tan 𝛼 =
𝑁𝑀
𝑃𝑁
4. Use postulates of congruence and similarity to
show that triangle ABC and ACD are congruent if
ABCD is a rectangle.
𝐴𝐶 is common to both triangles 𝐴𝐵 = 𝐶𝐷 (Opposite sides of a rectangle) 𝐴𝐷 = 𝐶𝐵 (Opposite sides of a rectangle) Since corresponding sides are equal, we have the postulate SSS hence the two triangles are congruent
5. Find the basic trigonometric ratios of 30°and
68°
tan 30° = 0.5774, sin 30° = 0.5, cos 30° = 0.866 tan 68° = 0.3746, sin 68° = 0.9271, cos 68° = 0.3746
6. Given that sin 𝜃 =1
3
a). Find 𝑐𝑜𝑠 𝜃 and tan 𝜃 (give the exact answer)
cos 𝜃 =2√2
3, tan 𝜃 =
1
2√2
b). Find sin(90° − 𝜃)
sin 𝜃 =2√2
3
N M
P
𝛼
A B
C D
Day 91 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 93
Use the following diagram to answer the following questions.
𝑇𝐵̅̅ ̅̅ = 17 𝑖𝑛, 𝑇𝐾̅̅ ̅̅ = 9 𝑖𝑛 .
1. Find the size of angle KTB in terms of 𝑟.
2. Find the length of 𝐾𝐵̅̅ ̅̅ .
3. Find tan 𝑟
4. Find cos ∠𝑇
5. Find csc 𝑟.
K T
B
𝑟
Day 91 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 94
Answer Keys
Day 91:
1. 90 − 𝑟
2. 14.42 𝑖𝑛
3. 0.6241
4. 0.5294
5. 1.889
Day 91 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 95
1. Draw any right angle triangle and label it as shown below.
2. Measure segments 𝐴𝐵̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅ and 𝐶𝐴̅̅̅̅ .
3. Measure the following angles ∠𝐴 and ∠𝐶
4. Find the sum of the angles in 3 above.
5. Use measurements in 2 above to find sine, cosine of ∠𝐷 and ∠𝐹.
6. Use measurements in 3 above to find sine, cosine of ∠𝐷 and ∠𝐹.
7. Compare the sine and cosine of ∠𝐷 and ∠𝐹 respectively
8. Compare the cosine and sine of ∠𝐷 and ∠𝐹 respectively
A B
C
Day 91 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 96
In this activity, students will draw a right angle and verify the equality of sine and cosine of
complementary angles. Each group will be composed of at least 3 students and will require a protractor,
a ruler, a pencil and a plain paper.
Answer Keys
Day 91:
1 No response
2. Different responses but must satisfy the Pythagorean theorem
3. Different responses but must add up to 90°.
4. They add up to 90°
5 - 6. Different responses
7. They are equal
8. They are equal
Day 91 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 97
Use the following information to answer questions 1 – 15
In the figure above, ABCD is a rectangle measuring 24 in by 10 in.
1.Find the length of AC.
2. Find cos ∠𝐵𝐴𝐶
3. Find cos ∠𝐴𝐶𝐵
4. Find sin ∠𝐵𝐴𝐶
5. Find sin ∠𝐴𝐶𝐵
6. Compare your answer in 2 and 5 above. What do you notice?
7. Compare your answer in 3 and 4 above. What do you notice?
A B
C D
Day 91 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 98
8. Find cos ∠𝐷𝐴𝐶
9. Find cos ∠𝐷𝐶𝐴
10. Find sin ∠𝐷𝐴𝐶
11. Find sin ∠𝐷𝐶𝐴
12. Compare your answer in 8 and 10 above. What do you notice?
13. Compare your answer in 9 and 11 above. What do you notice?
14. Identify a common feature that the angles whose ratios are being compared in 13 and 12 above
have?
15. What is your conclusion from the relations in 12, 13 and 14 above?
Day 91 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 99
Use the following information to answer questions 16 - 20
16. Find cos ∠𝑌
17. Find cos ∠𝑆
18. Find sin ∠𝑆
19. Find sin ∠𝑌
20. Compare your answers in 16 and 19 above and explain your answer.
T Y
S
56°
Day 91 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 100
Answer keys
Day 91:
1. 26 in
2. 0.9231
3. 0.3846
4. 0.3846
5. 0.9231
6. They are equal
7. They are equal
8. 0.3846
9. 0.9231
10. 0.9231
11. 0.3846
12. They are equal
13. They are equal
14. They add up to 90°
15. Sine and cosine of two complementary angles are equal
16. 0.5592
17. 0.8290
18. 0.5592
19. 0.8290
20. They are equal
Day 91 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 101
Find the sine and cosine of 𝛼 and 𝜃 respectively hence compare the answers.
𝜃
𝛼
9 𝑖𝑛
25 𝑖𝑛
Day 91 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 102
Answer Keys
Day 91
sin 𝛼 = 0.96
cos 𝜃 = 0.96
They are equal
Day 92 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 103
In right ∆PQR below, the measure of ∠P is given as 𝛼 and that of ∠R by 𝛽. Use it to determine the
following values:
(a) sin 𝛼
(b) cos 𝛼
(c) sin 𝛽
(d) cos 𝛽
(e) 𝛼 + 𝛽
Using the values above, identify one trigonometric ratio that is equal to:
(f) sin 𝛼
(g) cos 𝛼
R
P L 𝑐
𝑎
𝑏
𝛽
𝛼
Day 92 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 104
Answer keys:
Day 92:
(a) sin 𝛼 =𝑏
𝑎
(b) cos 𝛼 =𝑐
𝑎
(c) sin 𝛽 =𝑐
𝑎
(d) cos 𝛽 =𝑏
𝑎
(e) 90°
(f) cos 𝛽
(g) sin 𝛽
Day 92 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 105
1. Use the sine and cosine tables you have been provided with to find the sine and cosine of the
tabulated angles.
2. List all pairs of complementary angles from the tabulated angles above.
3. What do you notice about sin 10° and cos 80° from your values in the table above?
4. What do you notice about cos 10° and sin 80° from your values in the table above?
5. What do you notice about sin 20° and cos 70° from your values in the table above?
6. What do you notice about cos 70° and sin 20° from your values in the table above?
Angle Sine Cosine
10°
20°
30°
40°
50°
60°
70°
80°
Day 92 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 106
7. Compare the sine of one angle to the cosine of the other angle in each of the pairs of complementary
angles you have listed in 2 above. What do you notice?
8. Now, compare the cosine of one angle to the sine of the other angle in each of the pairs of
complementary angles you have listed in 2 above. What do you notice?
9. Try the process in 7 and 8 above for any two pairs of complementary angles of your choice. What
does this tell you about the sine and cosine of any pair of complementary angles?
Day 92 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 107
In this activity, students will work in groups of four to deduce the relationship between sine and cosine
of complementary angles using trigonometrical tables. The students should be equipped with
trigonometrical tables having sine and cosine tables. Note the values in the tables are given correctly to
four significant figures.
Answer keys Day 92:
1.
2. 10° and 80°
20° and 70°
30° and 60°
40° and 50°
3. sin 10° = cos 80°
4. cos 10° = sin 80°
5. sin 20° = cos 70°
6. cos 70° = sin 20°
7. The sine of one angle is equal to the cosine of the other angle in each pair
8. The cosine of one angle is equal to the sine of the other angle in each pair
9. The cosine of any angle is equal to the sine of its complement and the sine of any angle is equal to the
cosine of its complement.
Angle Sine Cosine
10° 0.7136 0.9848
20° 0.3420 0.9397
30° 0.5000 0.8660
40° 0.6428 0.7660
50° 0.7660 0.6428
60° 0.8660 0.5000
70° 0.9397 0.3420
80° 0.9848 0.7136
Day 92 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 108
Given that the pair of angles is acute, find the value of 𝜽 in questions 1-5.
1. cos 11° = sin 𝜃
2. sin 58° = cos 𝜃
3. cos(2𝜃 + 16°) = sin 2𝜃
4. sin(𝜃 − 36°) = cos 𝜃
5. cos 2𝜃 = sin(𝜃 + 18°)
6. In right ∆KLM, ∠L is the right angle and sin 𝑀 = 𝜃. What will be the value of cos ∠𝐾?
7. In right ∆PQR, ∠Q is the right angle and cos 𝑃 = 𝛼. What will be the value of sin 𝑅?
8. Given that sin(2𝑥 + 20°) = cos(𝑥 + 40°), find the measures of the two acute angles in the
corresponding right triangle.
9. In right ∆XYZ, ∠Y is the right angle and cos 𝑋 = 4𝑥 − 9 and sin 𝑍 = 3𝑥 − 6. Calculate the value of 𝑥.
10. In right ∆JKL, ∠K is the right angle and cos 𝐽 = 𝑥 and sin 𝐽 = 𝑦. Write an expression for
sin 𝐿 + cos 𝐿.
Day 92 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 109
11. Identify an angle measure where the sine and cosine have the same value.
12. Given that sin 60° =√3
2 and cos 𝛼 =
√3
2. Find 𝛼.
13. Given that sin 66° = 0.9135, find the cosine of the complementary angle.
14. Given that cos 23° = 0.9205, find the sine of the complementary angle.
In questions 15-20, solve for the unknown.
15. sin (5
2𝑦 + 12°) = cos (
1
2𝑦)
16. cos(7𝑧 + 15°) = sin(3𝑧 + 40°)
17. sin 𝑘 = cos 2𝑘
18. cos (1
3𝑛 + 2°) = sin 43°
19. sin(2𝑝 + 1°) = cos 44°
20. cos(5𝑥 + 10°) = sin(4𝑥 − 19°)
Day 92 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 110
Answer keys
Day 92:
1. 79°
2. 32°
3. 18.5°
4. 63°
5. 24°
6. 𝜃
7. 𝛼
8. 40° and 50°
9. 𝑥 = 3
10. 𝑥 + 𝑦
11. 45°
12. 30°
13. 0.9135
14. 0.9205
15. 𝑦 = 26°
16. 𝑧 = 3.5°
17. 𝑘 = 30°
18. 𝑛 = 135°
19. 𝑝 = 22.5°
20. 𝑥 = 11°
Day 92 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 111
Solve for 𝛼 in the following equations given that the angles are acute.
(a) sin(𝛼 − 54°) = cos 𝛼
(b) cos(𝛼 + 42°) = sin 2𝛼
Day 92 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 112
Answer keys
Day 92:
(a) 𝛼 = 72°
(b) 𝛼 = 16°
Day 93 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 113
1. Use the figure below to answer the questions that follow.
a) Use Pythagorean theorem to find the length of the side labeled 𝑏.
b) Calculate sin 30°
c) Calculate cos 30°
d) Calculate sin 60°
e) Calculate cos 60°
30°
60°
10 𝑖𝑛
20 𝑖𝑛
𝑏
Day 93 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 114
Answer Key Day 93:
1. a) 17.32 𝑖𝑛
b) 0.5
c) 0.866
d) 0.866
e) 0.5
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 115
In this activity, students will draw a right triangle and solve it using the trigonometric ratios. Students
will work in groups of at least three and each group is required to have a pencil, a ruler, a plain paper
and a compass.
1. Draw a line which is 4 𝑖𝑛 long and label it AB.
2. Construct a line perpendicular to AB passing through end A.
3. Construct a line making an angle of 60° with AB at point B and extend it to intersect with line
perpendicular to AB at point C.
4. Using trigonometric ratios, calculate the lengths of line AC and BC.
What are their lengths?
5. Using a ruler measure the length of line AC and BC.
What do you get? Are they equal to the results you got in step 4 above?
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 116
Answer Keys
Day 93:
1-3. No response
4. AC is about 7 𝑖𝑛
BC is about 8 𝑖𝑛
5. AC is about 7 𝑖𝑛
BC is about 8 𝑖𝑛
Yes
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 117
Use the figure below to answer questions 1-2.
1. Find the length of AB.
2. Find the length of BC.
Use the figure below to answer questions 3-4
3. Find the value of a.
4. Find the value of b.
A B
C
2 𝑖𝑛
45°
5 𝑖𝑛
20°
a
b
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 118
Use the diagram below to answer questions 5 and 6.
5. Find the value of c.
6. Find the value of d
Use the figure below to answer questions 7-12
𝑆𝑈 = 20 𝑖𝑛 and ∠𝑈𝑆𝑉 = 50°.
7. Find the length of ST.
8. Find the length of UV.
9. Find the size of angle T.
39°
15 𝑖𝑛
d
c
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 119
10. Calculate the length of SV
11. Calculate the length of UT.
12. Calculate the size of VT
Use the figure below to answer questions 13 to 18.
13. Find the length of MJ.
14. Find the length of JL.
15. Find the size of ∠𝐾.
16. Find the length of JK.
12 𝑖𝑛 20 𝑖𝑛 40°
K L
M
J
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 120
Use the figure below to answer questions 17 and 18.
17. Find the value of 𝑥
18. Find the value of 𝑦
19. Find the size of ∠𝑁
20. Find the value of 𝜃
75°
𝑥
𝑦
25 𝑖𝑛
M N
O
9 𝑖𝑛 7 𝑖𝑛
S T
U
18 𝑖𝑛
14 𝑖𝑛
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 121
Answer Key Day 93:
1. 2 𝑖𝑛
2. 2.83 𝑖𝑛
3. 13.74 𝑖𝑛
4. 14.62 𝑖𝑛
5. 18.52 𝑖𝑛
6. 23.84 𝑖𝑛
7. 31.1 𝑖𝑛
8. 15.3 𝑖𝑛
9. 40°
10. 12.8 𝑖𝑛
11. 23.8 𝑖𝑛
12. 18.3 𝑖𝑛
13. 26.11 𝑖𝑛
14. 16.8 𝑖𝑛
15. 54.4°
16. 20.63 𝑖𝑛
17. 6.47 𝑖𝑛
18. 24.15 𝑖𝑛
19. 51°
20. 38.9°
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 122
1. Use trigonometric ratios to find the value of 𝑥 in the figure below.
𝑥
30°
8 𝑖𝑛
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 123
Answer Keys Day 93:
1. 4 𝑖𝑛
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 124
In right ∆ABC below ∠C = 31° and AD = 24 𝑖𝑛. The figure is not drawn to scale and all lengths are in
inches.
(a) Find the measure of ∠A.
Calculate the length of the following sides, giving your answers correct to two decimal places.
(b) AB
(c) BD
(d) BC
(e) DC
A
B C
D
31°
24 𝑖𝑛.
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 125
Answer keys
Day 94:
(a) ∠A = 59°
(b) 46.60 𝑖𝑛.
(c) 39.94 𝑖𝑛.
(d) 77.56 𝑖𝑛.
(e) 66.48 𝑖𝑛.
Day 93 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 126
1. Measure the length of the wooden pole using the surveyor’s tape measure provided.
2. Record the length of the pole in the writing pad provided.
3. Let one member of your group hold the pole upright ensuring that the flat surface is properly aligned
to the ground.
4. Measure the length of the shadow formed by the pole using the tape measure.
5. Record the length of this shadow in the writing pad provided.
6. Record the time at the moment you are measuring the length of the shadow.
7. The sketch below represents a right triangle to depict