Question

An electrical tower casts a 120-foot shadow. At the same time, a 10-foot

street sign casts a shadow of 8 feet. What is the height of the tower?

Answer 1

Height of the tower = 150 foot

Explanation:

We need to find height of the tower with 120-foot shadow.

We have a 10-foot street sign casts a shadow of 8 feet.

`\texttt{Ratio of height to shadow height =}(10)/(8)=(5)/(4)`

We have

`\frac{\texttt{Height of tower}}{\texttt{Shadow height of tower}}=(5)/(4)\\\\\frac{\texttt{Height of tower}}{120}=(5)/(4)\\\\\texttt{Height of tower}=(5)/(4)* 120=150feet`

Height of the tower = 150 foot

Answer 2

The height of the tower is 150 ft

Explanation:

Let the height of the tower be H feet.

The corresponding sides will then be in the same proportion.

The ratio of the shadows will be in the same proportion as the ratio of the heights.

`(H)/(10)=(120)/(8)`

We multiply both sides by 10 to get:

`(H)/(10)* 10=(120)/(8)* 10`

`H=150`

Therefore, the height of the tower is 150 ft