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

30 ft

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