If a telephone pole casts a shadow 20 feet long and a person 6 feet tall casts a shadow 3 feet long. In feet, what is the height of the telephone pole?

Question

I want to know the height of the telephone pole and the options for it are: 

A. 10

B. 17

C. 23

D. 49

I don't know how to solve it.

Answer 1

I wish I could draw a picture for this, but I can't. Let h be the height of the telephone pole.

 

There are two similar triangles in the (undrawn) picture:

 

One has the telephone pole, its shadow, and the hypotenuse is the segment from the top of the pole to the tip of the shadow. The other has the person's height, his/her shadow, and the hypotenuse the segment from the top of the head of the person to the tip of their shadow. They are similar because the sun's angle of elevation is the same for both triangles, and they are also both right triangles.

 

Using a proportion,

 

h/20 = 6/3, 

 

you can solve and get the height of the pole as 40 ft.