Question

A 32 foot tall tree casts a shadow that is 48 feet long How far away from the tree is a 6 ft person

Answer 1

39

Explanation:

Answer 2

39 feet

Explanation:

In the attached diagram

The height of the tree = AB

The height of the man =DE

The length of the shadow =BC

We want to determine how far away from the tree the person is, i.e. |AD|=y

In Triangle ABC

`Tan \theta=(32)/(48)`

In Triangle CED

`Tan \theta=(6)/(48-y)`

Therefore:

`Tan \theta=(32)/(48)=(6)/(48-y)\\(32)/(48)=(6)/(48-y)\\$Cross Multiply\\32(48-y)=48*6\\1536-32y=288\\32y=1536-288\\32y=1248\\Divide both sides by 32\\y=39`

Therefore, the distance of the man from the tree is 39 feet.