CK-12 Geometry-Concepts

http://www.ck12.org Chapter 7. Similarity

Example C

The Empire State Building is 1250 ft. tall. At 3:00, Pablo stands next to the building and has an 8 ft. shadow. If he
is 6 ft tall, how long is the Empire State Building’s shadow at 3:00?

Similar to Example B, solve by setting up a proportion that compares height to shadow length. Then solve the
equation to find the length of the shadow. Letxrepresent the length of the shadow.

6 f t

8 f t

=

1250 f t

x

6 x= 10000

x= 1666. 67 f t

The shadow is approximately 1666.67 feet long.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52559

CK-12 Foundation: Chapter7IndirectMeasurementB

Concept Problem Revisited

It is safe to assume that George and the flagpole stand vertically, making right angles with the ground. Also, the
angle where the sun’s rays hit the ground is the same for both. The two trianglesare similar. Set up a proportion.

10

85

=

6

x

−→ 10 x= 510

x= 51 f t.

The height of the flagpole is 51 feet.

Vocabulary

Two triangles aresimilarif all their corresponding angles arecongruent(exactly the same) and their corresponding
sides areproportional(in the same ratio). Solve proportions bycross-multiplying.

Guided Practice

In order to estimate the width of a river, the following technique can be used. Use the diagram.