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Solving Word Problems
Use the 3 ratios – sin, cos and tan to
solve application problems.
Choose the easiest ratio(s) to use
based on what information you are
given in the problem.
Draw a Picture
When solving math problems, it can be
very helpful to draw a picture of the
situation if none is given.
Here is an example.
Find the missing sides and angles for
Triangle FRY. Given that angle Y is
the right angle, f = 68, and y = 88.
The picture helps to visualize
what we know and what we want
to find!
F
88
r
Y
R
68
1. From a point 80m from the base of a tower, the
angle of elevation is 28˚. How tall is the tower?
x
28˚
80
Using the 28˚ angle as a reference, we know opposite and adjacent sides.
opp
Use
adj
tan
tan 28˚ =
x
80
80 (tan 28˚) = x
80 (.5317) = x
x ≈ 42.5
About 43 m
2. A ladder that is 20 ft is leaning against the side
of a building. If the angle formed between the ladder
and ground is 75˚, how far will Ms. McGinnis have to
crawl to get to the front door when she falls off the
ladder (assuming she falls to the base of the ladder)?
building
20
75˚
x
Using the 75˚ angle as a reference, we know hypotenuse and adjacent side.
adj
x
Use
cos 75˚ =
cos
hyp
20
20 (cos 75˚) = x
20 (.2588) = x
x ≈ 5.2
About 5 ft.
3. When the sun is 62˚ above the horizon, a
building casts a shadow 18m long. How tall is
the building?
x
62˚
18 shadow
Using the 62˚ angle as a reference, we know opposite and adjacent side.
opp
x
Use
tan 62˚ =
tan
adj
18
18 (tan 62˚) = x
18 (1.8807) = x x ≈ 33.9
About 34 m
4. A kite is flying at an angle of elevation of about
55˚. Ignoring the sag in the string, find the height of
the kite if 85m of string have been let out.
kite
85
x
55˚
Using the 55˚ angle as a reference, we know hypotenuse and opposite side.
opp
x
Use
sin 55˚ =
sin
hyp
85
85 (sin 55˚) = x
85 (.8192) = x
x ≈ 69.6
About 70 m
5. A 5.50 foot person standing 10 feet from a street
light casts a 24 foot shadow. What is the height of the
streetlight?
5.5
10
tan x˚ =
5.5
14
x° ≈ 21.45°
14 shadow
x˚
tan 21.45 
height
24
About 9 ft.
Depression and Elevation
If a person on the ground
looks up to the top of a
building, the angle
formed between the line
of sight and the
horizontal is called the
angle of elevation.
angle of depression
angle of elevation
If a person standing on
the top of a building
looks down at a car on
the ground, the angle
formed between the
line of sight and the
horizontal is called the
angle of depression.
horizontal
horizontal
6. The angle of depression from the top of a tower to a
boulder on the ground is 38º. If the tower is 25m high,
how far from the base of the tower is the boulder?
38º
angle of depression
Alternate Interior Angles are congruent
25
38º
x
Using the 38˚ angle as a reference, we know opposite and adjacent side.
opp
Use
tan
tan 38˚ = 25/x
adj
(.7813) = 25/x
X = 25/.7813
x ≈ 32.0
About 32 m