Similarity and Indirect Measurement(5

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COURSE 3 LESSON 5-8
Similarity and Indirect Measurement
When a 6-ft student casts a 17-ft shadow, a flagpole casts a
shadow that is 51 ft long. Find the height of the flagpole.
Set up a proportion for the similar triangles.
Words
flagpole’s height
length of flagpole’s shadow
=
student’s height
length of student’s shadow
Let h = the flagpole’s height.
Proportion
17h = 6 • 51
17h
6 • 51
=
17
17
h = 18
h
6
51
17
=
Write the cross products.
Divide each side by 17.
Simplify.
The height of the flagpole is 18 ft.
5-8
COURSE 3 LESSON 5-8
Similarity and Indirect Measurement
In the figure below,
ABC ~
EDC. Find d.
Use similar triangles to set up a proportion involving the lengths
of corresponding sides.
ED
CD
=
AB
CB
ED corresponds to AB.
CD corresponds to CB.
d
141
=
416
312
Substitute.
312 • d = 416 • 141
Write the cross products.
5-8
COURSE 3 LESSON 5-8
Similarity and Indirect Measurement
(continued)
312d = 58,656
Simplify.
312d
58,656
=
312
312
Divide each side by 312.
58,656
312
Use a calculator.
188
The length of d is 188 m.
5-8
COURSE 3 LESSON 5-8
Similarity and Indirect Measurement
1. A 5-ft tall student casts a 12-ft shadow. A tree casts a
27-ft shadow. How tall is the tree?
11.25 ft tall
2. A 6-ft man casts a 9-ft shadow. A sculpture casts a 45-ft shadow. How
tall is the sculpture?
30 ft
5-8

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