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

Answer:

39 feet

Step-by-step 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

$Tan \theta=\dfrac{32}{48}$

In Triangle CED

$Tan \theta=\dfrac{6}{48-y}$

Therefore:

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

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