Question

A street light is mounted on a pole. The tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 30°. A woman standing in the opposite direction of the pole as the man was standing on the same street has a angle of elevation from the tip of her shadow to her head of 41°. If the two people are 40 feet apart, how far is the street light from the head of the woman?

Answer 1

21.15 ft

Explanation:

The angle at the lamp between the two shadow tips is ...

180° -30° -41° = 109°

This angle is opposite the 40-ft side of the triangle. The distance (d) in question is opposite the 30° angle, so can be found from the Law of Sines as ...

d/sin(30°) = 40'/sin(109°)

d = (40')·sin(30°)/sin(109°) ≈ 21.152'

The distance from the light to the woman's head is about 21.15 feet.

_____

We have to assume the heads are at the same height.