Angles of Elevation &
Depression Problems
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Do Now!
If the cos  
2
, find the value of the following :
5
(HINT: You may need Pythagorean Theorem)
Exact value
sin  
tan  
THE ANGLE OF ELEVATION
THE ANGLE OF DEPRESSION
Rounded to 4
decimals
Angles of Elevation &
Depression Problems
Example 1
Scott, whose eye level is 1.5 m above the ground, stands 30 m from a tree. The angle of elevation of a
bird at the top of the tree is 36˚. How far above ground is the bird?
Example 2
Standing on the gallery of a lighthouse (the deck at the top of a lighthouse), a person spots a ship at an
angle of depression of 20˚. The lighthouse is 28 m tall and sits on a cliff 45 m tall as measured from sea
level. What is the horizontal distance between the lighthouse and the ship? Sketch a diagram to
support your answer.
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Angles of Elevation &
Depression Problems
Now you try! Make sure to draw a diagram.
1) A 15 feet ladder leans against a wall at 52. How far from the wall is the foot of the ladder (to the
nearest foot)?
2) A little boy flies his kite. The string formes an angle of elevation of 37 and from where he stands to
directly under the kite is 45 ft. How long is the kite string (to the nearest ft)?
3) An airplane spots the floating debris at an angle of depression of 15. If the plane is at an altitude of
3,000 feet, what is the horizontal distance before they fly over it (to the nearest hundred feet)?
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Angles of Elevation &
Depression Problems
Problem Set
1) A young boy lets out 30 ft of string on his kite. If the angle of elevation from the boy to his
kite is 27°, how high is the kite?
2) To support a young tree, Jack attaches a guy wire from the ground to the tree. The wire is
attached to the tree 4 ft above the ground. If the angle formed between the wire and the tree
is 70°, what is the length of the wire?
3) A helicopter is directly over a landing pad. If Billy is 110 ft from the landing pad, and looks
up to see the helicopter at 65° to see it. How high is the helicopter?
4) A man in a lighthouse tower that is 30 ft. He spots a ship at sea at an angle of depression of
10°. How far is the ship from the base of the lighthouse?
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Angles of Elevation &
Depression Problems
5)Answer the following questions.
a) Using the drawbridge diagram, determine the distance from one side to the other. (exact
answer)
45°
40 ft
45°
40 ft
b) Now that you know the distance from side to side, determine how high the drawbridge
would be if the angle of elevation was 60.(exact answer)
60°
60°
40 ft
c) How far apart would the drawbridge be if the angle of elevation of the drawbridge was 20?
x
20°
20°
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