Transcript
Page 1: How do I use Trigonometry to solve word problems?

• How do I use Trigonometry to solve word problems?

Page 2: How do I use Trigonometry to solve word problems?

1.

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2. What is the length of the diagonal of a square with side lengths ?27

3. The length of the diagonal of a square is 22. What is the length of each side?

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4. 5.

6.

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7. A baseball "diamond" is a square of side length 90 feet. How far is the throw, to one decimal place, from home plate to second base?

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8. To find the height of a tower, a surveyor positions a transit that is 2 meters tall at a spot 95 meters from the base of the tower. She measures the angle of elevation to the top of the tower to be 32°. What is the height of the tower, to the nearest meter?

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9. A slide 4.1 m long makes an angle of 27° with the ground. How high is the top of the slide above the ground?

10. Liola drives 16 km up a hill that is at a grade of 10o. What horizontal distance, to the nearest tenth of kilometer, has she covered?

1.4x

27

10

16

x

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11.

12. A photographer shines a camera light at a particular painting forming an angle of 40° with the camera platform. If the light is 58 feet from the wall where the painting hangs, how high above the platform is the painting?

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13. A tree 19 feet tall casts a shadow which forms an angle of 49° with the ground. How long is the shadow to the nearest hundredth?

14. Find tan S.

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15. Find tan A for the right triangle below:

16. Use the diagram to find cos x as a fraction in simplest form.

17. Find tan B for the right triangle below:

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18. 19. Find sin A.

20. Write sin B.

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21. Use a calculator to find cos 17°, cos 37°, cos 57°, and cos 77°. As the angle increases, what happens to the cosine of the angle? Explain.

22. Find the value of x, to the nearest whole number. (not drawn to scale)

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23. Find sin P, cos P, tan P.

Write the trigonometric ratio.

a. sin Ab. tan Bc. cos A

24.

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25.

26. A 220 ft string attached to a kite makes a 30o angle with the ground. What is the height of the kite to the nearest tenth?

30

220 x

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27. A parasailing company uses a 50-foot cable to connect the parasail to the back of the boat. About how far is the parasail from the water when the cable has a 35° angle of elevation? Explain how you got your answer.

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28.

29. Solve using the diagram and the given measurements. (Note: The triangle is not drawn to scale.)B = 49°, a = 4

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31.

32.

Use a special right triangle to find the sine and cosine of the given angle.

30

45

60 45

30

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33.

34.

Assume that is an acute angle. If sin A = 0.9540, find tan A to four decimal places. (Use your calculator.)

Assume that is an acute angle. If sin A = 0.994, use a calculator to find the measure of to two decimal places.

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35.

36.

37.

Find the measure of an acute angle that satisfies the given equation. Round your answers to the nearest tenth of a degree.

tanY 409

sinX 611

cos Z 1213

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38.

Solve the right triangle:

. and , , find ;10 and 50 cba

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39. An antenna is atop the roof of a 100-foot building, 10 feet from the edge, as shown in the figure below. From a point 50 feet from the base of the building, the angle from ground level to the top of the antenna is 66°. Find x, the height of the antenna, to the nearest foot.

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40. An airplane is flying at an elevation of 1500 feet. What is the airplane's angle of elevation from the runway when it is 5000 feet from the runway? Explain.

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5.ex Trig Word Problems

Word Problem Worksheet


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