1. Similarity and Indirect Measurement
COURSE 3 LESSON 5-8
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
Let h = the flagpole’s height.
Proportion
flagpole’s height
student’s height
length of flagpole’s shadow
length of student’s shadow = h 6 51 17
17h = 6 • 51 Write the cross products.
Divide each side by 17.
17h 17
6 • 51 =
h = Simplify.
The height of the flagpole is 18 ft.
5-8

2. Similarity and Indirect Measurement
COURSE 3 LESSON 5-8
In the figure below, ABC ~ EDC. Find d. =
Use similar triangles to set up a proportion involving the lengths of corresponding sides. ED AB CD CB
ED corresponds to AB.
CD corresponds to CB. = d
416
141
312
Substitute.
312 • d = 416 • 141
Write the cross products.
5-8

3. Similarity and Indirect Measurement
COURSE 3 LESSON 5-8
(continued)
312d = 58,656
Simplify.
312d ,656 =
58,
Divide each side by 312.
Use a calculator.
The length of d is 188 m.
5-8

4. Similarity and Indirect Measurement
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?
2. A 6-ft man casts a 9-ft shadow. A sculpture casts a 45-ft shadow. How tall is the sculpture?
11.25 ft tall
30 ft
5-8