Welcome to Math 6+-x

Problem Solving Using Indirect Measurement

The Connector…

Distances or lengths that are difficult to measure directly can sometimes be found using the properties of similar polygons and proportions.

This kind of measurement is called indirect measurement.

OBJECTIVES:

Each student will:

1. Use properties of similar triangles to solve problems of indirect measurement.

Thales is known as the first Greek scientist, engineer, and mathematician.

Legend says that he was the first to determine the height of the pyramids in Egypt by examining the shadows made by the Sun.

He considered three points: • the top of the objects, • the lengths of the shadows, and • the bases.

We will use a proportion.

All of these problems involve the shadow that

is cast from an object.

It would be difficult to measure the

height of the tree directly.

GUIDED PRACTICE

Guided Practice 1

A statue casts a shadow 30 feet long. At the same time, a person who is 5 feet tall casts a shadow that is 6 feet long. How tall is the statue?

Guided Practice 2

A building casts a shadow 72 meters long. At the same time, a parking meter that is 1.2 meters tall casts a shadow that is 0.8 meters long. How tall is the building?

Indirect Measurement Worksheet

ASSIGNMENTS

Proportions are one of the most powerful concepts that you will find.

CONCLUSION

Which of the figures in the picture do you think would measure the tallest with a ruler?