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.

Write proportion of side lengths.

Cross Products Property

Solve for x.x = 80

40x = 64(50)

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

ANSWER

x ft64 in.

50 ft40 in.=

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?

58 in.

x

80

50 ft.

GUIDED PRACTICE for Example 3

Write proportion of side length

80x = 58 50

x = 36.25

Cross product property

Solve for x

SOLUTION

The flagpole and the child next to the women form sides of two right triangles with the ground, here, there are two pairs of congruent angles, so the triangles are similar by the AA similarity postulate.

You can use a proportion to find the length of the shadow (x).

58x = 80

50

GUIDED PRACTICE for Example 3

The length of the shadow is 36.25 in. long.

ANSWER

GUIDED PRACTICE for Example 3

SOLUTION

Tree height

Your height =

Length of your shadow

Length of shadow

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.