Related Rates Question: How to Use Similar Triangles to Solve for Shadow Length?

[jen333]

Hey, I have this one practise calculus question that I just can't seem to get. Any help would be greatly appreciated:

A light is on the ground 40ft from a building. A man 6ft tall walks from the light towards the building at 6ft/s. How rapidly is his shadow on the building becoming shorter when he is 20ft from the building?
(btw, the answer should be -3.6ft/s)

I've already drawn a diagram, but I'm not sure if triangle ratios would do any good.

 

[StatusX]

Were you able to find the height of his shadow as a function of his distance from the building?

 

[courtrigrad]

First draw a picture. You know its going to be a triangle. Let x be the distance the man is from the light. And let y be the height of his shadow on the building. You know dx/dt = 6. We also know that the length of the triangle is 40 ft. So we can divide the side into x + (40-x). So how would you use similar triangles to find y as a function of x?

Hint: $$\frac{6}{x} = \frac{y}{?}$$