Question

If a boy 5 feet tall casts a shadow 14 feet long, what will be the length of the shadow of a tree that is 25 feet high?

Answer 1

70 feet

Explanation:

This problem can be answered by using proportions based on similar triangles.

Notice that a person and its shadow on the ground form a right angle (therefore they can be considered the two "legs" of a right angle triangle)

The same runs for the tree and its shadow.

Since the inclination of the rays of the sun are the same at the same time for both objects (the boy and the tree), their hypothenuses form the same angles with the ground and therefore belong to similar triangles.

We can create the following proportion to solve for the shadow of the tree (ST) using the information provided: the height of the boy (HB), the shadow of the boy (SB), and the height of the tree (HT)

`(SB)/(HB) =(ST)/(HT)\\(14)/(5) =(ST)/(25)\\(ST)/(25)=(14)/(5) \\ST=(14*25)/(5)\\ST=70\,\,ft`