Question

A vertical pole 12 feet high casts a shadow 8 feet long on the ground. At the same time, a nearby tower casts a 40 feet long shadow on the ground.What is the height of the tower?

Answer 1

Find the ratio of height to shadow on the pole. It will be similar to the ratio of height to shadow length on the tower if it's the same time of day.

Solve

Answer 2

The height of the tower is 60 feet.

Explanation:

Given,

The vertical pole 12 feet high casts a shadow 8 feet long on the ground.

So, the ratio of the height of pole and height of its shadow =
`(12)/(8)`

Also, at the same time the tower casts a shadow of 40 feet long on the ground,

Let x be the height of the tower,

⇒ The ratio of the height of tower and height of its shadow =
`(x)/(40)`

Since, at the same time,

`(12)/(8)=(x)/(40)`

`480=8x` ( By cross multiplication )

`60=x` ( Dividing both sides by 8 )

Hence, the height of the tower is 60 feet.