Download Trigonometry Name Right Triangle Trigonometry Review UQ: How

Trigonometry
Right Triangle Trigonometry Review
Name
UQ: How can the definitions of the trigonometric functions be used to solve for missing parts of a right
triangle?
Covered Concepts:
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

What are the six basic trig functions and how can they be used to find the missing parts of
right triangles?
How can you find the missing sides and angles of a right triangle?
How can you solve for missing parts of a triangle in real life situations?
Questions
1. Find the complement of an angle that measures 73 degrees.
2. Find the supplement of an angle that measures 114 degrees.
3. Height of an evergreen tree. An evergreen tree casts a shadow that is 42.3 feet long. At the same time, a man
of height 67.5 inches casts a shadow that is 73.5 inches long. How tall is the evergreen tree?
4. Use the cofunction identity to fill in the blanks:
a. csc 15° = sec __°
b. tan23° = cot
__°
c. sin56° = cos
__°
5.
Use the right triangle diagram below and the information given to find the remaining measures.
Round your answers to two decimal places.
𝑎 = 10, 𝛼 = 41.7°
6. Distance across a lake. You can determine the distance across a lake without physically measuring it. You mark
off a right triangle on dry land and calculate the distance across the lake using a trigonometric function. If you
determine that one of the acute angles of the right triangle is 34°, and the side adjacent to the angle is 259 feet,
what is the distance across the lake? Round your answer to one decimal place.
7. If the longer leg of a 30° - 60° - 90° triangle has a length of √75, how long is the shorter side? Please make sure
to draw and label a picture of the special right triangle.
8. If the hypotenuse of a 45° - 45° - 90° triangle has a length of √8, how long are the legs? Please make sure to
draw and label a picture of the special right triangle.
9. Use a calculator to approximate the tan 37.2° to three decimal places.
10. Use a calculator to approximately the cot 157° to three decimal places.
11. Rewrite 47.321° as Degrees, Minutes and Seconds.
12. Evaluate cos 36°13’. Round answers to 3 decimal places.
13. Name the two trigonometric functions that have a value of
√3
2
on the interval 0° < x < 90°.
14. Use the right triangle diagram below and the information given to find the remaining measures.
Round your answers to two decimal places.
a = 20 in, c = 23 in
15. Roof Truss. A roofing contractor is building triangular roof trusses with a pitch of 45 degrees. If the hypotenuse
of the trusses is 104 feet, what is the number of linear feet of board required to build each truss (to the nearest
foot)?
16. Given the triangle below, find the value of the 3 trig functions.
17
θ
8
20
17. Given the tan x = 21 find the other five trig functions.
Sin x =
Cos x =
Cot x =
Sec x =
Csc x =
18. From a highway overpass, 15.7 meters above the road, the angle of depression of an oncoming car is measured at
17.4°. How far is the car from a point on the highway directly below the overpass?
17.4°
15.7 m
19. The angle of elevation of a pedestrian crosswalk over a busy highway is 9.52°. If the distance between the ends of
the crosswalk measured on the ground is 314 feet, then what is the height, h, of the crosswalk at the center?
20. A 37-meter guy wire is attached to the top of a 32.9-meter antenna and to a point on the ground. How far is the
point on the ground from the base of the antenna, and what angle does the guy wire make with the ground? Draw a
picture first!