Solving Right Triangles and Applications
Solve each right triangle. Round your answers to the nearest tenth.
R
1. A
2.
3.
C
A
35°
84.6
19
C
42.8
B
B
S
4.
M
55°
5.
T
15
6.
A
L
56
83.5
C
56.9
N
P
26.5
15.6
B
R
24.8
V
Solve each of the following. Sketch a picture where needed and show all work.
9. Find the length of a rectangle whose width is 78 and whose diagonal makes an angle
of 26 with the longer side. Round your answer to the nearest tenth.
10. A window washer 50 feet above the ground sees a parked car 153 feet away from him.
What is the angle of depression rounded to the nearest degree?
11. Find the measures of the angles of an isosceles triangle whose sides have lengths 10,
13 and 13. Round your answers to the nearest degree.
12. A surveyor standing 200 feet from the base of a tree has found
that the angle of elevation to the top of the tree is 15°. Find
the height of the tree to the nearest tenth of a foot.
15°

200 ft
13. You are designing a house in town that gets a lot of snow. You
need the roof to have at least a 45° slope. How long must the
roof be if it is 40 feet from the center of the house to the outside
wall? Round your answer to the nearest tenth of a foot.
14. A certain mountain is known to be about 3 miles high. From
your location, you notice that the angle of elevation to the
top of the mountain is 15°. To the nearest tenth of a foot,
how far are you from the bottom of the mountain?
x
45°
40
3 mi
15°
x
15. After hip surgery, a nurse elevated the patient’s leg using a
device that measures the degrees between the leg and the
horizontal. If this device is set at 45° and if it is 12 inches
from the patient’s hip to knee, how high is the leg elevated?
Round your answer to the nearest tenth of an inch.
16 yd
16. To find the width of a river, a surveyor has measured the
angle between the bank that he is on and a tree on the other
side. The angle is 75°. The surveyor also knows a 16 yard
measure shown to the right. Find the width of the river to the
nearest yard.
h
12
45°

75°
17. A ladder 8 feet long is leaning against a wall. It makes an angle of 65° with the
ground. How far up the wall is the top of the ladder? Round your answer to the
nearest tenth of a foot.
18. What is the angle of elevation of the sun when a flagpole 10 meters tall casts a
shadow 12.6 meters long? Round your answer to the nearest degree.
19. Find the measure of a diagonal of a rectangle whose length is 18 inches if the
diagonal makes an angle of 51 with the shorter side of the rectangle. Round your
answer to the nearest tenth of an inch.
20. A 9-foot ladder is leaning against a house. The base of the ladder is 3 feet from the
house. Find the measure of the angle that the ladder makes with the ground to the
nearest tenth of a degree.