1. Module 6

1.17. Page 2

Mathematics 10-3 Module 6: Lesson 4

Module 6: Triangles and Other Polygons

 

Get Started

 

In this activity you will review how to handle proportions involving more than one measurement unit.

 

Self-Check

 

Work with a partner, if possible.

 

This is an image of a slalom ski course showing posts and their shadows.

© Walter Quirtmair/21324926/Fotolia

Consider the following two similar triangles. A shed of unknown height, x, casts a shadow measuring 12 ft 6 in. At the same time, a 2-ft vertical post casts a shadow measuring 3 ft 3 in.

 

This illustration shows two right triangles. The base of each triangle is horizontal with a right angle at the left side. The other base angles are both marked with a single arc. The base of the triangle on the left measures 12 feet 6 inches. The base of the triangle on the right measures 3 feet 3 inches. The height of the triangle on the right is 2 feet. The height of the triangle on the left is marked as x.

 

How would you set up and solve a proportion to determine the height of the shed?

 

Method 1

 

First convert all measures to feet. Recall that 1 ft = 12 in.

 

 

 

 

Set up the proportion.

 

 

 

 

The height is approximately 7.7 ft.

 

Method 2

 

First convert all measures to inches. Then solve for x by answering SC 1 through SC 3.

 

SC 1. What are the measures in inches?

 

SC 2. Set up a proportion and solve for x in inches.

 

SC 3. Convert your SC 2 answer from inches to feet. Round to one decimal place.

 

Compare your answers.