INDIRECT MEASUREMENTUSING PROPORTIONS

Thales is known as thefirst Greek scientist, engineer, andmathematician. Legend says thathe was the first to determine the

height of the pyramids in Egypt byexamining the shadows made by

the Sun. He considered three points:the top of the objects, the lengths of

the shadows, and the bases.

1. What appears to be true aboutthe corresponding angles in the

two triangles?2. If the corresponding sides are proportional, what could you

conclude about the triangles?

Indirect measurement allows you to use properties of similar polygonsto find distances or lengths that are difficult to measure directly.

Thales’ shadow = Thales’ heightpyramid’s shadow pyramid height

EXAMPLE 2 Using Indirect Measurement

Height

Alma is 5 feet tall and casts a 7 foot shadow. At the same time, a tree casts a 14 foot shadow. The triangles formed are similar. Find the height of the tree. Prove using a proportion.

A person 5 feet 3 inches tall casts a 6 foot shadow. At the same time of day, a lamppost casts an 18 foot shadow. What is the height of the lamppost?