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Objective

Solve problems involving similar triangles

Vocabulary

Indirect measurement

A technique using proportions to find a measurement

Example 1 Use Shadow Reckoning

Example 2 Use Indirect Measurement

TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?

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Write a ratio of the shadows

A tree in front of Marcel’s house has a shadow 12 feet long

Tree 12 feetMarcel

Marcel has a shadow 3 feet long

3 feet

Write a ratio of the actual size of Marcel and the tree

TreeMarcel

h feet

Define the variable

Marcel is 5.5 feet

5.5 feet

TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?

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Tree 12 feetMarcel 3 feetTreeMarcel

h feet5.5 feet

Write a proportion using the 2 ratios

12 feet3 feet

= h feet5.5 feet

Cross multiply

3h3h =3h = 12(5.5)

TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?

1/2

Bring down 3h =12 feet3 feet

= h feet5.5 feet

3h = 12(5.5)

3h =

Multiply 12 5.5

3h = 66 Ask “what is being done to the variable?”

The variable is being multiplied by 3

Do the inverse operation on both sides of the equal sign

TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?

1/2

Bring down 3h = 6612 feet3 feet

= h feet5.5 feet

3h = 12(5.5)

3h = 3h = 66

3h = 66

Using the fraction bar, divide both sides by 3

3 3

Combine “like” terms

1 h

Bring down =

1 h =

Combine “like” terms

1 h = 22

TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?

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Use the Identify Property to multiply 1 h

3h = 66 3 3

1 h = 22

h

Bring down = 22

h = 22 Add dimensional analysish = 22 feet

Answer: The tree is 22 feet tall.

Jayson casts a shadow that is 10 feet. At the same time, a flagpole casts a shadow that is 40 feet. If the flagpole is 20 feet tall, how tall is Jayson?

Answer: 5 feet

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SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

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The prompt states the triangles are similar so can write ratios

Write a ratio of similar sides

C is congruent on both triangles and the right angles are congruent from C

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

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CD is similar to CB so write a ratio using their lengths

Large triangle 60 mSmall triangle 20 m

AB is similar to DE so write the 2nd ratio

Large triangleSmall triangle

48 m d m

Write a proportion using the 2 ratios

60 m20 m = 48 m

d m

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

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60 m20 m

= 48 m d m

Cross multiply the numbers60d60d = 60d = 20(48)

Bring down 60d =60d =

Multiply 20 4860d = 960

Ask “what is being done by the variable”?

The variable is being multiplied by 60

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

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60 m20 m

= 48 m d m

Do the inverse on both sides of the equal sign60d60d = 60d = 20(48)

60d = 60d = 960 Bring down 60d = 960

60d = 960 Using the fraction bar, divide both sides by 6060 60

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

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Combine “like” terms

60d = 960 60 60

1 d Bring down =1 d =

Combine “like” terms

1 d = 16

Use the Identify property to multiply 1 d

d

Bring down = 16

d = 16

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

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Add dimensional analysis

60d = 960 60 60

1 d 1 d = 1 d = 16 d d = 16 d = 16 m

Answer: The distance across the stream is 16 meters.

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the river.

Answer: 7 feet

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Lesson 4:7 Indirect Measurement 3 - 13 All

Assignment