What is the height of the tree?

Question

Charles places a mirror on the ground 63 feet  from the base of a tree. He walks backwards until he can see the top of the tree in the middle of the mirror. At that point, Jason's eyes are 6 feet above the ground and he is 9 feet from the image in the mirror. What is the height of the tree?

Answer 1

There are two possible answers depending on how the 9 ft is interpreted.   If the 9 ft is the distance along the ground between Charles and the mirror, the calculation is:

    6/9 = h/63      and  h = 42.

 

If the 9 ft is the distance from Charles' eye to the mirror, then the distance along the ground is sqrt(81-36) = 6.7 ft

   6/6.7 =  h/63   and  h = 56 ft.