6th Grade Math Textbook, Fundamentals

t

10 ft

4.5 ft

3 ft

 &KDSWHU

6-8

Update your skills. See page 410.

Indirect Measurement

Objective To solve problems involving indirect measurement by using similar right triangles

A tree casts a 10-ft shadow. At the same time, a 4.5-ft-tall

boy standing nearby casts a 3-ft shadow. How tall is the tree?

To find the height of the tree, use indirect measurement

to write and solve a proportion involving similar right triangles.

is used when the distance, height,

or length of an object is difficult to measure directly.

 Set up a proportion.

Let tthe tree’s height.

Solve: 

 Use the Cross-Products Rule.

3 t 10 • 4.5 Multiply.

 Divide both sides by 3.

t 15

So the tree is 15 ft tall.

4.5

t

3

10

Indirect measurement

45

3

3 t

3

4.5

t

3

10

boy’s height

tree’s height

boy’s shadow

tree’s shadow

Triangle ABCand triangle EDCare similar.

Find the distance across the lake along AB.

 Set up a proportion.

Let dthe length of AB.

Solve:  Substitute.

 Use the Cross-Products Rule.

6 d8 • 30 Multiply.

 Divide both sides by 6 to isolate d.

d 40

Check:

40(6) 8(30)

240  240 Tr u e

So the distance across the lake along ABis 40 meters.

30

6

d

8

Substitute 40 for d

? in the original equation.



30

6

(^40) ?
8
240
6
6 d
6
30
6
d
8
BC
DC
AB
ED
1
Check:
3(15) 10(4.5)
45  45 Tr u e
Substitute 15 for t
in the original equation.
?
4.5
15
(^3) ?
10
8 m
d
6 m
30 m
AB
C
ED