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Trigonometry with Right Triangles

Module Quiz: B

Use the figure for 1–2.

[pic]

1. Name the side opposite[pic]

2. Name the side adjacent to[pic]

Use the figure for 3–5.

[pic]

State each of the following:

3. What is tan[pic]

4. What is sin[pic]

5. What is cos[pic]

A right triangle is shown.

[pic]

6. If [pic] ’ 68°, what is GI? Show your work.

7. Are sin and cos reciprocals of each other? Explain.

8. Given that cos 42°[pic]0.743, what is the sine of the complementary angle?

Use the figure for 9–10.

[pic]

9. What is LK rounded to the nearest hundredth? Show your work.

10. What is JK rounded to the nearest hundredth? Show your work.

Use the figure for 11–12.

[pic]

11. What is [pic]

12. What is [pic]Explain how you got your answer.

Trigonometry with Right Triangles

Module Quiz: B

[pic]is shown.

[pic]

13. What are the missing side lengths in [pic]Explain.

[pic]is shown.

[pic]

14. What are the missing side lengths in [pic]Explain. Keep your answer in simplified radical form.

15. What is a Pythagorean Triple?

16. State whether the following are Pythagorean Triples or multiples of Pythagorean Triples.

A 6, 8, 10 [pic] Yes [pic] No

B 14, 48, 50 [pic] Yes [pic] No

C 25, 25, 100 [pic] Yes [pic] No

17. What is the area of [pic] to the nearest tenth?

[pic]

18. Solve the triangle by finding the lengths of all the sides and the measures of all the angles. Show your reasoning.

[pic]

19. Find the side lengths to the nearest hundredth and the angle measures to

the nearest degree.

[pic]

MODULE 13 Trigonometry with Right Triangles

Module Quiz 13: B

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic] 2 tan 68° ’ GI; GI [pic] 4.95

7. No; Sin of an angle is equal to the opposite side divided by the hypotenuse. Cosine of an angle is equal to the adjacent side divided by the hypotenuse. Both are divided by the hypotenuse so they are not reciprocals of each other.

8. 0.743

9. [pic] 8.5(sin 20°) ’ LK; LK [pic] 2.91

10. [pic] JK(tan 20°) ’ 2.91; JK [pic] 8

11. [pic] [pic]

12. The sum of the interior angles of a triangle are 180, so [pic] ’ 180° − 90° − 27° ’ 63°.

13. In a 45-45-90 triangle, the hypotenuse is [pic] times each leg. So, [pic] and QR [pic] 8.49.

14. TU ’ [pic] SU ’ [pic] [pic]

15. A Pythagorean triple is a set of 3 positive integers such that a2 + b2 ’ c2.

16. A Yes B Yes C No

17. [pic]

18. To find [pic] sin x ’ [pic] so, [pic] Then [pic] ’ 90° − 59° ’ 31°. To find DF, 52 + (DF)2 ’ (5.83)2 or DF is about 2.998 ft.

19. [pic] so [pic]

AB ’ 4, BC ’ 8, [pic] [pic]

[pic] and [pic] are complementary, so [pic]

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