Geometry PAP
Test Review Unit 8 (7.5-7.7)
For # 1 – 6, find each ratio using the picture to the right. Write the answer as a fraction in
lowest terms.
A
1. sin A
2. cos A
17
3. tan A
4. sin B
8
5. cos B
6. tan B
C
15
B
Find sin x, cos x, and tan x for each of the following. Write the answer as a fraction in lowest
terms.
x
26
10
7.
xx
8.
x
14
x
9.
10.
48
Solve the following.
11. Draw right triangle ABC with a right angle at B. If tan C 
9
, then cos A  ______ .
40
12. Use triangle PQR with side lengths p, q, r to answer the following
P
sin R  ______ = cos______
fraction with letters
letter
r
q
Q
R
p
For each of the following 13 - 18, solve for x. If x is a side length, round to three decimal places. If x is an
angle measure, round to a whole number.
13.
14.
x
8
12
65°
51°
x
15.
16.
58°
x
x°
25
28
22
17.
18.
x°
x
18
62°
21
25
Answer each of the following. Round lengths to three decimal places and angles to a whole number.
19. A damsel is in distress and is being held captive in a tower. Her knight in shining armor is on the
ground below with a ladder. When the knight stands 15 feet from the base of the tower and looks up at
his precious damsel, the angle between the ladder and the ground is 60 degrees. How long is the ladder
so that it rests on the tower?
20. The shadow of a telephone pole is 20 feet long. You measure the angle of elevation from the end of
the shadow to the top of the telephone pole to be 70°. What is the height of the telephone pole?
21. A forest ranger stands at an observation window 70 feet above the ground. She sees a fire in the
distance. She takes a reading of the angle of depression and finds it to be 24°. How far away from the
base of the tower is the fire?
70 ft
22. A wheelchair ramp provides a 2 foot increase over the course of 16 feet. Find:
A) The length of the ramp.
2 ft
16 ft
B) The angle of elevation for the ramp (round to a whole degree).
C) If regulations say a wheelchair ramp can be no more than 10°, what is the shortest length the ramp
could have?
23. Calculate the perimeter
I0 cm
24. A man whose eyes are 6 feet from the ground sees a window-washer on the side of a building 150
feet from where he is standing. The angle of elevation from the man’s line of sight to the windowwasher is 20 degrees. The next time the man looks up, the window-washer is at a 25 degree angle of
elevation. How many feet did the window-washer move up the building?
Find the missing sides in each triangle for 25 & 26 using special right triangle ratios.
25.
3 2
18
12
4 3
5 6
26.
30°
60°
4
30°
60°
12
5 3
30°
6 3
6 6
26. Each triangle on the dragon’s tail is a 45-45-90 or 30-60-90 triangle. The sum of the squares of the
variable is the year that China’s Ming Dynasty began. Show answers for a-j and determine the year.
a______
b______
c_____
d_____
e_____
f_____
g_____
h_____
i_____
j_____
year: ______
27. Complete the unit circle and use it to answer the questions to the side.
sin 45  _____
cos330  _____
tan 270  _____
sin135  _____