Indirect measurement

Course 3

5-7 Indirect Measurement5-7 Indirect Measurement

Course 3

Warm UpWarm Up

Lesson PresentationLesson Presentation

Course 3

5-7 Indirect Measurement

Warm UpSolve each proportion.

x75

35

=1. 2.48

6x

=2.

x6

9 27

=3. 87

x3.5

=4.

x = 45 x = 20

x = 2 x = 4

Course 3


Learn to find measures indirectly by applying the properties of similar figures.

Course 3


Vocabulary

indirect measurement

Course 3


Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.

Course 3


Additional Example 1: Geography Application

Triangles ABC and EFG are similar.

Triangles ABC and EFG are similar. Find the length of side EG.

B

A C

3 ft

4 ft

F

E G

9 ft

x

Course 3


Additional Example 1 Continued

ABAC = EF

EG Set up a proportion.

Substitute 3 for AB, 4 for AC, and 9 for EF.

3x = 36 Find the cross products.

The length of side EG is 12 ft.x = 12

Triangles ABC and EFG are similar. Find the length of side EG.

34 = 9

x

3x3 = 36

3 Divide both sides by 3.

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Check It Out: Example 1

Triangles DEF and GHI are similar.

Triangles DEF and GHI are similar. Find the length of side HI.

2 in

E

D F

7 in

H

G I

8 in x

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Check It Out: Example 1 Continued

DEEF = GH

HI Set up a proportion.

Substitute 2 for DE, 7 for EF, and 8 for GH.

2x = 56 Find the cross products.

The length of side HI is 28 in.

x = 28

27 = 8

x

2x2 = 56


Triangles DEF and GHI are similar. Find the length of side HI.

Course 3


A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree?

Additional Example 2: Problem Solving Application

11 Understand the Problem

The answer is the height of the tree.

List the important information:

• The length of the building’s shadow is 75 ft.

• The height of the building is 30 ft.

• The length of the tree’s shadow is 35 ft.

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Use the information to draw a diagram.22 Make a Plan

h

Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

Solve3375 feet

30 feet

35 feet

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30 75

= h35

Solve33

Corresponding sides of similar figures are proportional.

75h = 1050 Find the cross products.

The height of the tree is 14 feet.

h = 14

75h75 = 1050



Course 3


Since = 2.5, the building’s shadow is

2.5 times its height. So, the tree’s shadow should also be 2.5 times its height and 2.5 of 14 is 35 feet.

44 Look Back

75 30


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A 24-ft building casts a shadow that is 8 ft long. A nearby tree casts a shadow that is 3 ft long. How tall is the tree?

Check It Out: Example 2

11 Understand the Problem

The answer is the height of the tree.

List the important information:

• The length of the building’s shadow is 8 ft.

• The height of the building is 24 ft.

• The length of the tree’s shadow is 3 ft.

Course 3


Use the information to draw a diagram.22 Make a Plan

h

Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

Solve33

3 feet

8 feet

24 feet


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24 8

= h3

Solve33

Corresponding sides of similar figures are proportional.

72 = 8h Find the cross products.

The height of the tree is 9 feet.

9 = h

728 = 8h



Course 3


Since = , the building’s shadow is

times its height. So, the tree’s

shadow should also be times its

height and of 9 is 3 feet.

44 Look Back

8 24

1 3

1 3

1 3

1 3


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1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river?

2. A yardstick casts a 2-ft shadow. At the same

time, a tree casts a shadow that is 6 ft long. How

tall is the tree?

Lesson Quiz

7.98 m

9 ft

w

7 m

5 m

5.7 m

Indirect measurement

Business

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