developed by Vicki Borlaug

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Word Problems Finding a Side
of a Right Triangle (given a side and an angle)
developed by Vicki Borlaug Walters State
Community College Summer 2008
Note to Instructor These word problems do not
require Law of Sines or Law of Cosines.
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Question developed by V. Borlaug WSCC, 2008
Not drawn to scale.
Example 1.) A straight boat ramp is being
designed to cover a horizontal distance of 150
feet with an angle of elevation of 3º. Find the
length of the boat ramp.
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Example 2.) A hot air balloon rises vertically.
Katie is standing on the level ground 20 feet
from a point on the ground where the balloon was
launched. She points her camera at the balloon
and takes a picture. When Katie takes the
picture the camera is 5.5 feet off the ground and
has a 80º angle of elevation . Find the height
of the hot air balloon when the picture is taken.
Question developed by V. Borlaug WSCC, 2008
Not drawn to scale.
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Example 3.) A crane has a 100 foot arm with a
hook at the end of the arm. This crane is
designed so that the angle of elevation of the
arm can be changed. When the cranes hook is
attached to an object on the ground, the arms
angle of elevation is 5º. The cranes arm then
rotates upward and raises the object to a
position that gives the arm a 25º angle of
elevation. Find the height the crane has lifted
the object. HINT Find the tip of the arms
initial distance from horizontal. Then find the
distance from horizontal after the object has
been lifted. Use these to find the height the
object has been lifted.
Not drawn to scale.
Question developed by V. Borlaug WSCC, 2008
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Example 4.) Derek is scuba diving in still
water. Starting from the surface he dives in a
straight line with a 65º angle of depression.
Derek is traveling at a constant rate of 25 feet
per minute along this straight line path. a.)
Find the distance Derek has traveled along this
straight line path three minutes into the
dive. b.) Find Dereks vertical depth three
minutes into the dive. c.) Find the rate at
which Dereks vertical depth is changing as he
descends.
Question developed by V. Borlaug WSCC, 2008
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Example 5.) A river runs between a tree and a
lamp post. The tree is directly north of the
lamp post. The surveyor is 324 feet east of the
lamp post. He measures an angle
of 11.3º from the tree to the lamp post. Find
the distance from the surveyor to
the tree.
Question developed by V. Borlaug WSCC, 2008
Not drawn to scale.
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Example 6.) Jessica is standing 75 feet from the
base of a vertical tree. She is 5 ½ feet tall
and her eyes are 4 inches from the top of her
head. It takes a 38º angle of elevation for
Jessica to look at the top of the tree.
(Use four decimal place accuracy.) a.)
Find the height of the tree in feet. b.) Find
the height of the tree in meters.

NOTE One meter is the length equal to
1,650,763.73 wavelengths in a vacuum of the
orange-red radiation of krypton 86. One meter
also equals 39.37 inches.
Ref The American Heritage Dictionary of the
English Language, American Publishing Co., Inc.,
1969
Question developed by V. Borlaug WSCC, 2008
Not drawn to scale.
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Example 7.) A helicopter is hovering 560 feet
above a straight and level road that runs east
and west. On the road east of the helicopter are
a car and a truck. From the helicopter the angle
of depression to the car is 48º and the angle of
depression to the truck is 38º. Find the
distance between the car and the truck.
HINT First find the distance from a point
directly below the helicopter to the car. Then
do the same for the truck. Use these to find the
distance between the car and the truck.
Question developed by V. Borlaug WSCC, 2008
Not drawn to scale.
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Example 8.) A boat is due south of a light
house. From his charts the captain knows that
the light house is 0.76 miles east of the pier.
The captain takes measurements from his boat and
finds an angle of 55º from the light house to the
pier. a.) Find the distance from the boat to
the pier. b.) Find the distance from the boat to
the light house.
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Example 9.) A straight 67 inch ramp is being
designed for a skate board course. a.) Find the
vertical height required to give the skate board
ramp a 75º angle of depression. b.) Find the
vertical height required to give the skate board
ramp a 65º angle of depression. c.) Find the
vertical height required to give the skate board
ramp a 55º angle of depression.
Question developed by V. Borlaug WSCC, 2008
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Example 10.) A helicopter takes off from ground
level and goes 853 feet with an angle of
elevation of 23º. The helicopter then changes
course and goes 719 feet with and angle of
elevation of 49º and then it hovers in this
position. Find the height of the hovering
helicopter.
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Example 11 A short building is 200 feet away
from a taller building. Jessie is on the roof of
the short building. To see the top of the taller
building requires Jessie to look up with a 38?
angle of elevation. To see the bottom of the
taller building requires Jessie to look down with
12? angle of depression. Find the height of the
taller building. (You may assume that Jessies
height is negligible.)

HINT To solve begin by making two separate
right triangles.
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Example 12 Solar panels are being installed on
a roof. The roof has an angle of elevation of
9.2º. Each solar panel is 7.20 feet long and
4.80 feet wide. The longer edge of each panel
will be horizontally installed on the roof. The
shorter edge of the panel will be installed with
an angle of elevation 29.6º. a.) Find the
vertical height of each solar panel relative to
horizontal. b.) Find the vertical height of each
solar panel relative to the roof directly the
solar panels highest edge.
Hint for part b Using the two angles of
elevation there here are two right triangles.
First solve the larger right triangle completely.
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Answers
1) Cos 3 150 X
X 150.2
X
3
150
2) Tan 80 X 20 X
113.4 113.4 5.5 118.9
X
80
20
15
Answers
3) Sin 5 X 100 X
8.7 Sin 25 Y 100
Y 42.3 Height 42.3 8.7 Height 33.6
Feet
100
X
5
100
Y
25
16
Answers
65
X
75
c) 68.0 / 3 22.7 ft per min
4)
a) 3 x 25 75
b) Sin 65 X X 68.0
75
17
Answers
T
X
11.3
L
S
324
5)
Cos 11.3 324 X X 330.4
18
Answers
X
38
75
5 ft 2 inches
6)
Height 95.1764 5.1667 100.3431 feet
or 100.3431 / 39.37 2.5488 meters
Cos 38 75 X X 95.1764 5 2
5.1667ft
19
Answers
48
H
38
560
48
38
T
C
X
Y
7)
Tan 38 560 Y Y 716.8
Tan 48 560 X X 504.2
Distance 716.8 504.2 212.6
20
Answers
Sin 55 .76 X X .93
8)
.76
L
P
Y
55
X
B
Tan 55 .76 Y Y .53
21
Answers
Sin 65 X 67 X 60.7
X
67
75
9)
Sin 75 X 67 X 64.7
Sin 55 X 67 X 54.9
22
Answers
719
Y
49
853
X
23
Sin 49 Y 719 Y 542.6
Sin 23 X 853 X 333.3
10)
333.3 542.6 875.9
23
Answers
200
X
38
12
Y
Tan 12 Y 200 Y 42.5
Tan 38 X 200 X 156.3
11)
156.3 42.5 198.8
24
Answers
4.80
X
cos 29.6 Y 4.8 Y
4.17
Z
29.6
9.2
Y
12)
Sin 29.6 X 4.8 X 2.4
tan 9.2 Z 4.17 Y 0.7
2.4 0.7 1.7