Transcript Slide 1

5-7
5-7 Indirect
IndirectMeasurement
Measurement
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
5-7 Indirect Measurement
Warm Up
Solve each proportion.
1. 3 = x
5
75
3. 9 = x
27
Course 3
6
x = 45
x=2
2.
6 = 2.4
x
8
4. x = 8
3.5
7
x = 20
x=4
5-7 Indirect Measurement
Problem of the Day
A plane figure is dilated and gets 50%
larger. What scale factor should you use
to dilate the figure back to its original
size? (Hint: The answer is not 12.)
2
3
Course 3
5-7 Indirect Measurement
Learn to find measures indirectly by
applying the properties of similar figures.
Course 3
5-7 Indirect Measurement
Vocabulary
indirect measurement
Course 3
5-7 Indirect Measurement
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
5-7 Indirect Measurement
Additional Example 1: Geography Application
Triangles ABC and EFG are similar. Find the
length of side EG.
F
B
9 ft
3 ft
A
4 ft
C
E
x
Triangles ABC and EFG are similar.
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G
5-7 Indirect Measurement
Additional Example 1 Continued
Triangles ABC and EFG are similar. Find the
length of side EG.
AB = EF
AC
EG
Set up a proportion.
3
9
=
4
x
Substitute 3 for AB, 4 for
AC, and 9 for EF.
3x = 36
Find the cross products.
3x = 36
Divide both sides by 3.
3
3
x = 12
The length of side EG is 12 ft.
Course 3
5-7 Indirect Measurement
Check It Out: Example 1
Triangles DEF and GHI are similar. Find the
length of side HI.
H
E
2 in
D
x
8 in
7 in
F
G
Triangles DEF and GHI are similar.
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I
5-7 Indirect Measurement
Check It Out: Example 1 Continued
Triangles DEF and GHI are similar. Find the
length of side HI.
DE = GH
EF
HI
2
8
=
7
x
2x = 56
Set up a proportion.
Substitute 2 for DE, 7 for
EF, and 8 for GH.
Find the cross products.
2x = 56
Divide both sides by 2.
2
2
x = 28
The length of side HI is 28 in.
Course 3
5-7 Indirect Measurement
Additional Example 2: Problem Solving Application
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?
1
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.
Course 3
5-7 Indirect Measurement
Additional Example 2 Continued
2
Make a Plan
Use the information to draw a diagram.
h
30 feet
35 feet
3
Course 3
75 feet
Solve
Draw dashed lines to form triangles. The
building with its shadow and the tree with its
shadow form similar right triangles.
5-7 Indirect Measurement
Additional Example 2 Continued
3
Solve
30 = h
75
35
Corresponding sides of similar
figures are proportional.
75h = 1050
Find the cross products.
75h = 1050
75
75
Divide both sides by 75.
h = 14
The height of the tree is 14 feet.
Course 3
5-7 Indirect Measurement
Additional Example 2 Continued
4 Look Back
75
Since 30 = 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.
Course 3
5-7 Indirect Measurement
Check It Out: Example 2
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?
1
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
5-7 Indirect Measurement
Check It Out: Example 2 Continued
2
Make a Plan
Use the information to draw a diagram.
h
24 feet
3 feet
3
Course 3
8 feet
Solve
Draw dashed lines to form triangles. The
building with its shadow and the tree with its
shadow form similar right triangles.
5-7 Indirect Measurement
Check It Out: Example 2 Continued
3
Solve
24 = h
8
3
Corresponding sides of similar
figures are proportional.
72 = 8h
Find the cross products.
72 = 8h
8
8
Divide both sides by 8.
9=h
The height of the tree is 9 feet.
Course 3
5-7 Indirect Measurement
Check It Out: Example 2 Continued
4 Look Back
8
1
Since 24 = 3 , the building’s shadow is
1
3 times its height. So, the tree’s
shadow should also be 1 times its
3
1
height and 3 of 9 is 3 feet.
Course 3
5-7 Indirect Measurement
Lesson Quiz
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?
7.98 m
w
5m
7m
5.7 m
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?
Course 3
9 ft