how do i use trigonometry to solve word problems?

• How do I use Trigonometry to solve word problems?

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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?

4. 5.

6.

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?

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?

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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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?

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.

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:

18. 19. Find sin A.

20. Write sin B.

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)

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

Write the trigonometric ratio.

a. sin Ab. tan Bc. cos A

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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

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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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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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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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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36.

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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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Solve the right triangle:

. and , , find ;10 and 50 cba

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.

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.

5.ex Trig Word Problems

Word Problem Worksheet