Question

7 POINTS!!! ~ A 6 foot tall man casts a shadow that is 4.5 feet long. A telephone pole casts a shadow that is 15.6 feet long. Two similar triangles are created. How tall is the telephone pole?

Answer 1

Hello!

The answer is:

The telephone pole is 20.8 foot tall.

Why?

Since it's not mentioned, we can assume that both, man and the telephone pole are close, so, if two similar triangles are created, we know that both shadows are proportional and we can find the telephone pole height creating a proportionality relationship.

We can find the telephone pole height using the following equation,

$\frac{ManHeight}{ManShadow}=\frac{PoleHeight}{PoleShadow}$

Were,

Man height is 6 foot

Man shadow  is 4.5 feet long

Telephone pole shadow is 15.6 feet long.

So, substituting we have:

$\frac{6}{4.5}=\frac{PoleHeight}{15.6}$

$PoleHeight=15.6*\frac{6}{1.5}=20.8ft$

So, the telephone pole is 20.8 foot tall.

Have a nice day!