Anna is standing near a tree on a sunny day. She figures that she can calculate the height of the tree if she measures her shadow and the tree's shadow, and then uses a proportion.

Why can she use a proportion?

Anna can use a proportion because she and her shadow make two legs of a triangle that is similar to the triangle formed by the tree and its shadow.

Scroll over the images to see the triangles. Drag the meter sticks over the images to measure them.

Copy the following table into your notes. Fill in the missing information.

	Anna	Tree
Height	1.75 meters	h
Shadow	2.5 meters	40 meters

Use the information in the table to write a proportional relationship that could be used to solve for h, the height of the tree.

There are two ways to form the proportion:

Solve your proportion to determine the height of the tree.

tree's height over tree's shadow tree's height tree's shadow   =   Anna's height over Anna's shadow Anna's height Anna's shadow

 

h over 40 h 40   =   1.75 over 2.5 1.75 2.5

tree's height over Anna's height tree's height Anna's height   =   tree's shadow over Anna's shadow tree's shadow Anna's shadow

 

h over 1.75 h 1.75   =   40 over 2.5 40 2.5

(Note: consider your answer correct if you can match one of the answers by taking reciprocals of both ratios, switching sides of the equal sign, or both)

Solve your proportion to determine the height of the tree. Click on either method to see the full solution.