LESSON

How can you use similar shapes to find unknown measures?

Using Similar Shapes4.2

ADDITIONAL EXAMPLE 1∆QRS ~ ∆BCD. Find the unknown measurements.

Find the unknown side, x.1. 7.5 m

2. 30°Find m y.

ADDITIONAL EXAMPLE 2The rectangles shown are similar. Find the length of the larger rectangle. 120 m

ADDITIONAL EXAMPLE 3A billboard that is 60 feet tall is near a flagpole. The flagpole has a shadow that is 14 feet long at the same time that the shadow of the billboard is 24 feet long. Find the height of the flagpole. 35 ft

The shapes in each pair are similar. Find the unknown measures.

4.2 LESSON QUIZ7.5.A

t = 32 cm, d = 34°

1.

The shapes in each pair are similar. Find the unknown measures.

x = 16.5 ft, S = 29°

2.

3.

x = 110 cm

40 feet

A cell phone tower and a fence are on the same property. The fence is 8 feet tall and has a shadow that measures 14.5 feet. The shadow of the cell phone tower measures 72.5 feet. How tall is the cell phone tower?

4.

Will is standing in the shadow of a 40 foot tall telephone pole. He is standing so that his shadow and the telephone pole’s shadow end at the same place. The shadow of the telephone pole measures 64 feet. If Will is 5 feet 6 inches tall, how far away from the telephone pole is he? Explain.

55.2 feet; Will is 5 feet 6 inches tall, or 5.5 feet tall. Write a proportion using corresponding sides of the similar triangles . Solve for the length of Will’s shadow, which is 8.8 feet. Since the telephone pole’s shadow is 64 feet long, subtract to find how far from the telephone pole Will is. 64 – 8.8 = 55.2

How can you use similar shapes to find unknown measures?

Sample answer: To find an unknown length, write a proportion using corresponding sides. To find an unknown angle, compare it to the corresponding angle on the similar shape.