Penn Foster Trigonometry exam

Exam: 007694RR - RIGHT TRIANGLE

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Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.

1. Solar panels are used to convert energy from the sun into electricity. To get the best result, the panel has to be perpendicular to the sun's rays; in other words, angle θ has to be a right angle. What should the height, h, be if θ is a right angle, a solar panel is 12 ft long, and the sun's angle of elevation is 38°?

A. 9.4 ft

B. 15.4 ft

C. 7.4 ft

D. 9.5 ft

2. In a right triangle with g the right angle, a = 69.2° and c = 28.3. What is b? A. 19.2

B. 26.5

C. 20.8

D. 10.0

3. A carpenter wants to be sure that the corner of a building is square and measures 6.0 ft and 8.0 ft along the sides. How long should the diagonal be? A. 11 ft

B. 10 ft

C. 14 ft

D. 12 ft

4. A stairway must be built to a deck that is 20 feet above ground level. To the nearest half foot, how far from the base of the deck, on ground level, should the beginning of the stairway be placed so that the stairway forms a 60° angle from the ground? A. 12 ft

B. 35 ft

C. 11.5 ft

D. 11 ft

5. When viewing Angel Falls (the world's highest waterfall) from Observation Platform A, located on the same level as the bottom of the waterfall, we calculate the angle of elevation to the top of the waterfall to be 69.30°. From Observation Platform B, which is located on the same level exactly 1000 feet from the first observation point, we calculate the angle of elevation to the top of the waterfall to be 52.90°. How high is the waterfall? A. 2,646 ft

B. 1,322 ft

C. 998.5 ft

D. 2,643 ft

6. How many degrees does Earth turn during an eight-hour school day? (Assume that Earth makes one revolution every 24 hours.) A. 8°

B. 3°

C. 120°

D. 90°

7. A wheel 5.00 ft in diameter rolls up a 15.0° incline. How far above the base of the incline is the top of the wheel after the wheel has completed one revolution? A. 13.1 ft

B. 4.07 ft

C. 9.07 ft

D. 8.13 ft

8. In the triangle with g = 90°, β = 57.4°, and a = 70.0, which of the following measures is not correct? (Hint: Solve the triangle.) A. b = 109

B. c = 130

C. a = 32.6° D. c = 134

9. What is sin θ?

A. 0.571

B. 0.575

C. 0.496

D. 0.495

10. Find the numerical measure of the largest angle of a triangle whose angle measures are 6x – 10°, 3x + 30°, and 2(45° – x). A. 60°

B. 70°

C. 10°

D. 50°

11. A 16-foot ladder on ground level is leaning against a house. If the base of the ladder is placed 5.0 feet from the house, what is the angle formed at the top of the ladder? A. 18°

B. 72°

C. 24°

D. 20°

12.

A. x = 15

B. x = 10

C. x = 16

D. x = 12

13. In a right triangle with g the right angle, b = 86.5 and c = 125.8. What is β ? A. 43.4°

B. 46.4°

C. 46.6°

D. 43.2°

14. Which of the following pairs of angles are coterminal? A. 100° and 620°

B. 25° and –25°

C. 30° and 60°

D. 390° and 750°

15. A surveyor must divert her path from point C by proceeding due south for 300 ft to point A. The surveyor determines that point B, which is due east of point C, is N49°E from point A. What is the distance from point C to point B? A. 375 ft

B. 370 ft

C. 350 ft

D. 360 ft

16. Find the height of the Barrington Space Needle if the angle measured from the ground 1000 ft (measured to the nearest foot) from the point on the ground directly below the top of the needle is 58.15°. A. 621.2 ft

B. 1,610 ft

C. 1,895 ft

D. 527.7 ft

17. Find the approximate value of x for the pieces of the truss shown in this figure.

A. 15 ft, 11 in.

B. 14 ft, 2 in.

C. 16 ft, 3 in.

D. 15 ft, 7 in.

18. Which angle measure is consistent with all of the following criteria?

(i) The reference angle is 40°.

(ii) The angle is more than one revolution.

(iii) The angle's terminal side is in Quadrant II.

(iv) The angle isn't positive. A. –220°

B. 500°

C. –500°

D. –580°

19. A 6.00-foot person is casting a shadow of 4.20 feet. What time of the morning is it if the sun rose at 6:15 AM and will be directly overhead at 12:15 PM? A. 9:55 AM

B. 8:35 AM

C. 8:58 AM

D. 9:40 AM

20. Convert 21°50" to decimal degrees. Round your answer to the nearest thousandth. A. 21.833°

B. 21.014°

End of exam

C. 21.0138°

D. 21.8333°