Question

The Santa Cruz lighthouse casts a shadow 28 m long at 7 P.M. At the same time, the shadow of the lighthouse keeper, who is 1.75 m tall, is 3.5 m long. How tall is the lighthouse?

Answer 1

14 m

Explanation:

Here the angle of depression is same for light house as well as light house keeper at 7 P.M.

Let the angle be `theta`

For the keeper, height is 1.75 m and shadow is 3.5 m away from him. Hence `tan theta` = height/base = 1.75/3.5 = 1/2.

Now for the light house, shadow i.e. base is 28m and `tan theta` is 1/2. We have to find the height.

Hence, height= base x `tan theta`= 28 x 1/2 = 14 m