Question

At the same time a 6.5-foot-tall teacher casts a 9-foot shadow, a nearby flagpole casts a 31.5-foot shadow. How tall is the flag pole.

Answer 1

Answer: 1.86 ft.

Explanation:

Let x be the height of tree.

Given: A tree casts a 6.5 ft shadow at the same time that a person 9 ft tall casts a 31.5 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,

`(x)/(6.5)=(9)/(31.5)`

⇒
`x=(9*6.5)/(31.5)`

⇒
`x=1.86`

Hence, the height of the tree is 1.86 ft.

Answer 2

The shadow will be 38.5