# 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?

Oct 21, 2017

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