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Warm-Up Warm-Up Pg. 462 #59

Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

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Page 1: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Warm-UpWarm-Up

Pg. 462

#59

Page 2: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Warm-UpWarm-Up

Page 3: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Warm-UpWarm-Up

Cos Cos = adjacent / hypotenuse = adjacent / hypotenuse

oppositeopposite

hypotenusehypotenuse

2020

2929adjacentadjacent

aa22 + 20 + 2022 = 29 = 2922

aa22 = 29 = 292 2 - 20- 2022

aa22 = 441 = 441a = 21a = 21

Use Pythagorean Theorem Use Pythagorean Theorem to find the missing (opposite) side.to find the missing (opposite) side.

Page 4: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Warm-UpWarm-Up

Cos Cos = adjacent / hypotenuse = adjacent / hypotenuse

oppositeopposite

hypotenusehypotenuse

2121

2929adjacentadjacent

2020

Page 5: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Assignment QuestionsAssignment Questions

Page 6: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Lesson 8-4 Lesson 8-4 Trigonometry Trigonometry

pp. 456-462

Page 7: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

ObjectivesObjectives

• Find trigonometric ratios using right triangles.• Solve problems using trigonometric ratios.

Page 8: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

BenchmarksBenchmarks

• 1b. Given exact irrational solutions, determine the best rational estimation. (DOK 2)

• 1c. Solve real-world or application problems that involve square roots and the Pythagorean Theorem. (DOK 3)

• 4b. Solve real-world applications and mathematical problems to find missing measurements in right triangles by applying special right triangle relationships, geometric means, or trigonometric functions. (DOK 2)

• 4e. Apply the relationships of sine, cosine, and tangent to problems involving right triangles. (DOK 2)

Page 9: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

NoteNote

You can use trigonometric ratios to find the missing measures of a right triangle if you know the measures of two sides of a triangle or the measure of one side and one acute angle.

Page 10: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Check Your ProgressCheck Your Progress p. 458p. 458

3. Jonathan is standing 15 yards from a roller coaster. The angle formed by the ground to the top of the roller coaster is 71. How tall is the roller coaster?

Draw a pictureDraw a pictureto representto representthe situation!the situation!

Page 11: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Check Your ProgressCheck Your Progress p. 458p. 458

3. Jonathan is standing 15 yards from a roller coaster. The angle formed by the ground to the top of the roller coaster is 71. How tall is the roller coaster?

15 yd71°

Label theLabel thegiven info!given info!

x

Page 12: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Which ratioWhich ratiouses adjacent uses adjacent and opposite?and opposite?

Check Your ProgressCheck Your Progress p. 458p. 458

3. Jonathan is standing 15 yards from a roller coaster. The angle formed by the ground to the top of the roller coaster is 71. How tall is the roller coaster?

15 yd

TANGENT!!!TANGENT!!!

71°

x

Page 13: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Check Your ProgressCheck Your Progress p. 458p. 458

3. Jonathan is standing 15 yards from a roller coaster. The angle formed by the ground to the top of the roller coaster is 71. How tall is the roller coaster?

15 yd71°

x

Solve for x!Solve for x!43.6 yards43.6 yards

Page 14: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

Mid-Chapter QuizMid-Chapter Quiz p. 463p. 463

10. Find x to the nearest tenth.

32x

53

Label SidesLabel SidesWhich ratio usesWhich ratio usesadj & hyp?adj & hyp?COSINE!!!COSINE!!!Solve for x!Solve for x!53.253.2

Page 15: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

QuestionsQuestions

Page 16: Warm-Up Pg. 462 #59. Warm-Up Warm-Up Cos = adjacent / hypotenuse opposite hypotenuse 20 29 adjacent a 2 + 20 2 = 29 2 a 2 = 29 2 - 20 2 a 2 = 441 a

AssignmentAssignment

PracticePractice

Pg. 460-461 Pg. 460-461

#24, 25, 44, #24, 25, 44, 46, 47, 4846, 47, 48

Extra PracticeExtra Practice

GeometryOnline.com GeometryOnline.com

Self-Check QuizSelf-Check QuizLesson 8-4Lesson 8-4


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