Name
Mrs. Cullum
Geometry
Trig Ratio Worksheet
Find the indicated measures. Round segment lengths to the nearest tenth and angle measures to the nearest
whole number.
1.
2.
x
x •
8
4.
3.
X ~
w
y
y
5.
6.
12
y
y
7.
7.2
B
20.
y
y~
16
B
x
10.
h*_
9.
W'.
12
y
X ~
y~
Z ''
110
11. How tall is the tree?
12. How high is the kite?
13. A ladder 14 feet long rests against the side of a building. The base of the ladder rests on level ground
2 feet from the side of the building. What angle does the ladder form with the ground?
14. A 20-foot wire anchored to the ground braces a 17-foot pole. The wire is attached to the pole 15 feet
above the base of the pole. What angle does the wire make with the ground?
15. A road rises 10 feet for every 400 feet along the pavement. What is the measurement of the angle the
road forms with the horizontal.
16. The directions for the use of a ladder recommend that for maximum safety, the ladder should be placed
against a wall at a 75° angle with the ground. If the ladder is 14 feet long, how far from the wall should
the base of the ladder be placed?
17. Suppose the sun casts a shadow off a 35-foot building. If the angle of elevation to the sun is 52 , how
long is the shadow?
18. From her position in a hot-air balloon, Angie can see her car parked in a field. If the angle of depression
is 8° and Angie is 38 meters above the ground, what is the straight-line distance from Angie to her car?
19. A student can see a water tower from the closest point of the soccer field at her high school. The edge of
the soccer field is about 110 feet from the water tower and the water tower stands at a height of
32.5 feet. What is the angle of elevation if the eye level of the student viewing the tower from the edge
of the soccer field is 6 feet above the ground?
20. Stephan is standing on a mesa at the Painted Desert. The elevation of the mesa is about 1380 meters and
Stephan's eye level is 1.8 meters above ground. If Stephan can see a band of multicolored shale at the
bottom and the angle of depression is 29 , about how far is the band of shale from his eyes?
Name
Geometry
Trig Ratio Worksheet
Mrs. Cullumf
Find the indicated measures. Round segment lengths to the nearest tenth and angle measures to the nearest
whole number.
i.
2.
X«
y
y
36
|r
3.
•bnfrf**J2
C:
/
y
6.
5.
y»
10
70
11. How tall is the tree?
- K
12. How high is the kite?
S-3SV X
(
<)
"'
13. A ladder 14 feet long rests against the side of a building. The base of the ladder rests on level ground
2 feet from the side of the building.^ What angle does the ladder form with the ground?
14. A 20-foot wire anchored to the ground braces a 17-foot pole. The wire is attached to the pole 15 feet
above the base__of the pole. What angle does the wire make with the ground?
\
15. A road risesU) feet for every 400 feet along the pavement. What is the measurement of the angle the
road forms with the horizontal.
/ \
) 0
16. The directions for the use of a ladder recommend that for maximum safety, the ladder should be placed
against a wall at a 75° angle with the ground. If the ladder is 14 feet long, how far from the wall should
the base of the ladder be placed?
Cos 7S I
I
L*
&
;S
X
o
,4!-
17. Suppose the sun casts a shadow off a 35-foot building. If the angle of elevation to the sun is 52 , how
long is the shadow?
1 8. From her position in a hot-air balloon, Angie can see her car parked in a field. If the angle of depression
is 8° and Angie is 38 meters above the ground, what is the straight-line distance from Angie to her car?
x=38/sin 8 = about 273.0 ft
Straight line distance would mean the hypotenuse.
19. A student can see a water tower from the closest point of the soccer field at her high school. The edge of
the soccer field is about 110 feet from the water tower and the water tower stands at a height of
32.5 feet. What is the angle of elevation if the eye level of the student viewing the tower from the edge
of the soccer field is 6 feet above the ground?
tan-1(26.5/110)= about 13.5 degrees
20. Stephan is standing on a mesa at the Painted Desert. The elevation of the mesa is about 1380 meters and
Stephan's eye level is 1.8 meters above ground. If Stephan can see a band of multicolored shale at the
bottom and the angle of depression is 29 , about how far is the band of shale from his eyes?
x=1381.8/sin29 = about 2850.2 m