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

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 28°. 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 24°. If the two people are 20 feet apart, how far is the street light from the head of the woman?

Answer 1

OK. We don't know where the street light is. So let's say

 

h = height of street light

 

And although we know the man and woman are 20 ft apart, we don't know how close either is to the pole. So let's say

 

x = distance of woman from pole, 20-x = distance of man from pole

 

So what we have is this:

 

tan 24 = x/h = 0.445

tan 28 = (20 - x)/h = 0.532

 

We can rearrange this:

 

x = 0.445 h

20 - x = 0.532 h

 

And we can use these relations to find h:

 

20 = 0.977 h or h = 20.5 ft

 

Substituting gives

x = woman's position = 9.1 ft from pole,

leaving the man 10.9 feet away. Done!