Question

A tree casts a 9 ft shadow at the same time that a person 6 ft tall casts a 4 ft shadow. what is the height of the tree?

Answer 1

the height of the tree is 13.5 feet tall.

Answer 2

Answer: 13.5 ft.

Step-by-step explanation:

Let x be the height of tree.

Given: A tree casts a 9 ft shadow at the same time that a person 6 ft tall casts a 4 ft shadow.

Since both the tree and the man are standing vertical to the ground at the same time so the sun rays will make the same angle , therefore, the triangles made by both tree and man are similar.

And  in the similar triangles, the sides are proportional.

Therefore,

$\frac{x}{9}=\frac{6}{4}\\\Rightarrow\ x=\frac{6\times9}{4}\\\Rightarrow\ x=13.5$

hence, the height of the tree is 13.5 ft.