evaluating algebraic expressions 5-6 indirect measurement extension of mg1.2 construct and read...

Evaluating Algebraic Expressions

5-6 Indirect Measurement

Extension of MG1.2 Construct and read drawings and models made to scale.

California Standards



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.


5-6 Indirect MeasurementAdditional 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


5-6 Indirect MeasurementAdditional 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.


5-6 Indirect MeasurementCheck 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


5-6 Indirect MeasurementCheck 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.



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.


5-6 Indirect MeasurementAdditional Example 2 Continued

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

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

Solve33

h

35 feet

75 feet

30 feet



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


Additional Example 2 Continued



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

Additional Example 2 Continued



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.



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

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

Solve33

Check It Out! Example 2 Continued

h

3 feet

8 feet

24 feet



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





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


evaluating algebraic expressions 5-6 indirect measurement extension of mg1.2 construct and read...

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