It’s spirit week at school and your team wants to decorate the light
poles in the front of the building with strings of pennants in your
school’s colors. The pennants are strung together and sold by the
foot. To know how many feet of pennants to buy, you need to know
the height of the light poles.
1. The student who will be used for a
comparison is 5 feet and 11 inches tall. The
shadow cast by the student is 15 feet long.
The shadow cast by the light pole is 88 feet
long. You will use drawing tools to create and
label a model of the student and a light pole.
15 ft.
X
5’11 ft.
88 ft.
Work Out
Equation= 520.08=x15
1.
5.91
15
X
88
2. 5.91*88=520.8 and 15*x=? Because
we don’t know how tall the light post is.
3. 520.08=x15
÷15
÷15
x=34.67
Word Form
The light pole is 34.67 ft. tall.
X=34.67 ft.
6. Find the ratio of height to shadow to determine the height of the light.
The ratios you constructed should look like this. Remember to change all
units to inches.
5 feet 11 inches
h feet
=
15 feet
88 inches
SO in inches
71 inches
180 inches
=
h inches
1056 inches
In equation
180h=74976
H=416.53
Think
&
Discuss
1. There are six light poles in
the front of school. Will you be
able to buy enough flags for
each of the poles if they cost
$0.80 per foot and you have
$155.00 to spend on the
project?
Yes and $150.2 will be left over.
Try
This!
1. Complete the following
ratios to compute the height
of the
missing side of these right
triangles.
a. 5
20
=
h
120
So 600=h20 h=30
b. H
9
=
So 63=21h
7
21
h=3
2. On a separate piece of paper, draw an illustration and show the
ratio for a redwood tree that is 200 feet in height that casts a
shadow 500 feet long.
200 ft
500 ft
6 ft
H
36 m
13 ft
1. Use similar triangles to find the
height of the building.
1. H
6
39
13
2. So 234=13h
H=16
3m
H
4m
36 m
2. Use similar triangles to find the
height of the tree
1. 3
h
4
36
2. So 108=4h
H=27
3. A lamppost casts a shadow that is 15 yards long. A 3-foottall mailbox casts a shadow that is 5 yards long. How tall is
the lamppost?
1.h
3
15
5
2. So 40=5h
3 ft
H
15 Yards
H=8
5 Yards
4.An 8-foot-tall statue stands in the park and casts a shadow
that is 16 feet long. A dog stands next to it and is 3 feet tall.
How long is the dog's shadow?
1. h
16
3
8
2. So 48=8h
8 ft
H=6
3 ft
h
16 ft
5. A building casts a shadow that is 420 meters long. At the
same time, a person who is 2 meters tall casts a shadow that
is 24 meters long. How tall is the building?
1. h
24
420
2
2. So 840=2h
H=420
h
420 m
2m
24 m
6. On a sunny day around noon, a tree casts a shadow that is 12 feet long. At
the same time, a person who is 6 feet tall standing beside the tree casts a
shadow that is 2 feet long. How tall is the tree?
1. 6
h
2
12
2. So 72=2h
H=36
h
12 ft
6 ft
2 ft
7. A pole casts a shadow that is 21 feet long. A 3-feet-tall
child standing next to the pole casts a shadow that is 9 feet
long. How tall is the pole?
1. 3
h
9
21
2. So 63=9h
H=7
9 ft
h
3 ft
21 ft
8. Jeremy has two trophies next to each other sitting in the window of his
room. His football trophy is 7 inches tall and his basketball trophy is
13 inches tall. As the light shines in, the basketball trophy’s shadow
measures 26 inches. How long is the football trophy’s shadow?
1. h
26
2. So 182=13h
7
13
7 inches
13 inches
H=14
h
26 inches