• How do I use
Trigonometry to
solve word
problems?
1.
2. What is the length of the diagonal of a square with side lengths 7 2 ?
3. The length of the diagonal of a square is 22. What is the length of
each side?
4.
6.
5.
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?
x
4.1
27
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?
16
10
x
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?
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.
20. Write sin B.
19. Find sin A.
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.
24. Write the trigonometric ratio.
a. sin A
b. tan B
c. cos A
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?
220
30
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.
28.
29. Solve using the diagram and the
given measurements.
(Note: The triangle is not drawn to
scale.)
B = 49°, a = 4
Use a special right triangle to find the sine and cosine of the given angle.
30. 30
30
31. 45
32. 60
45
33. Assume that is an acute angle. If sin A = 0.9540, find tan A to four
decimal places. (Use your calculator.)
34. Assume that is an acute angle. If sin A = 0.994, use a calculator to
find the measure of to two decimal places.
Find the measure of an acute angle that satisfies the given equation.
Round your answers to the nearest tenth of a degree.
35. tanY  40
9
6
36. sinX 
11
37. cos Z 
12
13
Solve the right triangle:
38.   50 and a  10; find  , b, and c.
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