The light from a lamp casts shadow of a man standing 10 feet away from the lamppost. The shadow is 5 feet long. The angle of elevation from the tip of the shadow to the lamp is 50 degrees. How tall is the lamppost, to the nearest foot?

1 Answer
Sep 5, 2016

Height = #18# feet

Explanation:

In the triangle formed by the light from the lamp, we have the following information.

A 90° angle (assume the lamppost is vertical)

The angle of elevation of the top of the lamppost is 50°

The base is 15 feet long: the man is 10 feet away and his shadow is another 5 feet long. (adjacent side)

Using trigonometry we can find the height of the lamppost .(opposite side)

#(opp)/15 = tan 50°#

#opp = 15 tan 50°#

height = #17.88# feet