EXAMPLE 3 Standardized Test Practice EXAMPLE 3 Standardized Test Practice SOLUTION The flagpole and the woman form sides of two right triangles with the ground, as.

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Transcript EXAMPLE 3 Standardized Test Practice EXAMPLE 3 Standardized Test Practice SOLUTION The flagpole and the woman form sides of two right triangles with the ground, as.

Slide 1

EXAMPLE 3

Standardized Test Practice

EXAMPLE 3

Standardized Test Practice

SOLUTION
The flagpole and the woman form sides of two right
triangles with the ground, as shown below. The sun’s
rays hit the flagpole and the woman at the same
angle. You have two pairs of congruent angles, so the
triangles are similar by the AA Similarity Postulate.

EXAMPLE 3

Standardized Test Practice

You can use a proportion to find the height x. Write 5
feet 4 inches as 64 inches so that you can form two
ratios of feet to inches.
x ft = 50 ft
40 in.
64 in.
40x = 64(50)
x = 80

Write proportion of side lengths.
Cross Products Property
Solve for x.

ANSWER
The flagpole is 80 feet tall. The correct answer is C.

GUIDED PRACTICE

for Example 3

4. What If ? A child who is 58 inches tall is standing next
to the woman in Example 3. How long is the child’s
shadow?
ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE
5.

You are standing in your backyard, and you
measure the lengths of the shadows cast by both
you and a tree. Write a proportion showing how
you could find the height of the tree.

SAMPLE ANSWER
tree height
your height

=

length of shadow
length of your shadow


Slide 2

EXAMPLE 3

Standardized Test Practice

EXAMPLE 3

Standardized Test Practice

SOLUTION
The flagpole and the woman form sides of two right
triangles with the ground, as shown below. The sun’s
rays hit the flagpole and the woman at the same
angle. You have two pairs of congruent angles, so the
triangles are similar by the AA Similarity Postulate.

EXAMPLE 3

Standardized Test Practice

You can use a proportion to find the height x. Write 5
feet 4 inches as 64 inches so that you can form two
ratios of feet to inches.
x ft = 50 ft
40 in.
64 in.
40x = 64(50)
x = 80

Write proportion of side lengths.
Cross Products Property
Solve for x.

ANSWER
The flagpole is 80 feet tall. The correct answer is C.

GUIDED PRACTICE

for Example 3

4. What If ? A child who is 58 inches tall is standing next
to the woman in Example 3. How long is the child’s
shadow?
ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE
5.

You are standing in your backyard, and you
measure the lengths of the shadows cast by both
you and a tree. Write a proportion showing how
you could find the height of the tree.

SAMPLE ANSWER
tree height
your height

=

length of shadow
length of your shadow


Slide 3

EXAMPLE 3

Standardized Test Practice

EXAMPLE 3

Standardized Test Practice

SOLUTION
The flagpole and the woman form sides of two right
triangles with the ground, as shown below. The sun’s
rays hit the flagpole and the woman at the same
angle. You have two pairs of congruent angles, so the
triangles are similar by the AA Similarity Postulate.

EXAMPLE 3

Standardized Test Practice

You can use a proportion to find the height x. Write 5
feet 4 inches as 64 inches so that you can form two
ratios of feet to inches.
x ft = 50 ft
40 in.
64 in.
40x = 64(50)
x = 80

Write proportion of side lengths.
Cross Products Property
Solve for x.

ANSWER
The flagpole is 80 feet tall. The correct answer is C.

GUIDED PRACTICE

for Example 3

4. What If ? A child who is 58 inches tall is standing next
to the woman in Example 3. How long is the child’s
shadow?
ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE
5.

You are standing in your backyard, and you
measure the lengths of the shadows cast by both
you and a tree. Write a proportion showing how
you could find the height of the tree.

SAMPLE ANSWER
tree height
your height

=

length of shadow
length of your shadow


Slide 4

EXAMPLE 3

Standardized Test Practice

EXAMPLE 3

Standardized Test Practice

SOLUTION
The flagpole and the woman form sides of two right
triangles with the ground, as shown below. The sun’s
rays hit the flagpole and the woman at the same
angle. You have two pairs of congruent angles, so the
triangles are similar by the AA Similarity Postulate.

EXAMPLE 3

Standardized Test Practice

You can use a proportion to find the height x. Write 5
feet 4 inches as 64 inches so that you can form two
ratios of feet to inches.
x ft = 50 ft
40 in.
64 in.
40x = 64(50)
x = 80

Write proportion of side lengths.
Cross Products Property
Solve for x.

ANSWER
The flagpole is 80 feet tall. The correct answer is C.

GUIDED PRACTICE

for Example 3

4. What If ? A child who is 58 inches tall is standing next
to the woman in Example 3. How long is the child’s
shadow?
ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE
5.

You are standing in your backyard, and you
measure the lengths of the shadows cast by both
you and a tree. Write a proportion showing how
you could find the height of the tree.

SAMPLE ANSWER
tree height
your height

=

length of shadow
length of your shadow


Slide 5

EXAMPLE 3

Standardized Test Practice

EXAMPLE 3

Standardized Test Practice

SOLUTION
The flagpole and the woman form sides of two right
triangles with the ground, as shown below. The sun’s
rays hit the flagpole and the woman at the same
angle. You have two pairs of congruent angles, so the
triangles are similar by the AA Similarity Postulate.

EXAMPLE 3

Standardized Test Practice

You can use a proportion to find the height x. Write 5
feet 4 inches as 64 inches so that you can form two
ratios of feet to inches.
x ft = 50 ft
40 in.
64 in.
40x = 64(50)
x = 80

Write proportion of side lengths.
Cross Products Property
Solve for x.

ANSWER
The flagpole is 80 feet tall. The correct answer is C.

GUIDED PRACTICE

for Example 3

4. What If ? A child who is 58 inches tall is standing next
to the woman in Example 3. How long is the child’s
shadow?
ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE
5.

You are standing in your backyard, and you
measure the lengths of the shadows cast by both
you and a tree. Write a proportion showing how
you could find the height of the tree.

SAMPLE ANSWER
tree height
your height

=

length of shadow
length of your shadow