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Transparency 7. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 7-2c. Objective. Solve problems involving similar triangles. Example 7-2c. Vocabulary. Indirect measurement. A technique using proportions to find a measurement. - PowerPoint PPT PresentationTRANSCRIPT
Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.
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?
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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?
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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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