Question

A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4feet. Find the height of the tree.

Answer 1

Answer:

30 ft

Step-by-step explanation:

This is a problem of similar triangles.

         | \

         |    \

         |      \

     h  |        \

         |          \

         |         5|\

         |           | 4\

          <----24---->

      tree     man

The height of the man is 5 ft.

The shadow of the tree is 24 ft.

The shadow of the man is 4 ft.

We have similar triangles, so the lengths of their sides are proportional.

h/24 = 5/4

Cross multiply.

4h = 24 * 5

Divide both sides by 4.

h = 6 * 5

h = 30

Answer: 30 ft