A post is casting a shadow on the ground.

Question

A post is casting a shadow on the ground. If the post is 3 ft taller than the shadow on the ground, and the tip of the shadow is 15ft from the top of the post, how tall is the post?

Answer 1

s = length of shadow

s + 3 = height of pole    These are two legs of a right triangle. The hyspotenuse is 15

 

s² + (s + 3)² = 15²

s² + s² + 6s + 9 = 225

2s² + 6s - 216 = 0

2(s² + 3s - 108) = 0

s² + 3s - 108 = 0

(x + 12)(s - 9) = 0

 

{-12, 9}       Measurement is always positive.

 

The shadow is 9 feet and the height of the pole is 12.