Distance Problem

Question

A four foot tall child is standing near a 15 foot tall pole. Find an equation for the functions s(x) that gives the length of the child's shadow as a function of her distance from the base of the pole.

Answer 1

I will assume that there is a light at the top of the pole that produces the shadow.

 

The end of the shadow to the child and the end of the shadow to the pole are sides of similar triangles.

 

x = distance of child to the pole.

s = length of child's shadow.

 

s/4 = (s + x)/15

 

15s = 4s + 4x

 

11s = 4x

 

s = 4x/11