Calculating Shadow Movement Rates for a Walking Man Near a Light Source

[Geekchick]

Homework Statement

A man 6 feet tall walks as a rate of 5 feet per second away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light,
a) At what rate is the tip of his shadow moving?
b) At what rate is the length of his shadow changing?

Homework Equations

I know I have to use implicit differentiation

The Attempt at a Solution

Honestly I have no clue how to set up the equation. I'm good at implicit derivatives but I'm not so good at word problems.

Any help would be great!

 

[Dick]

Draw a picture and label some variables. Call D the man's distance from the base of the light and S the length of his shadow. Can you write an equation relating D and S. Think of similar triangles.

 

[Geekchick]

I'm don't mean to be difficult but i just don't see it.

 

[Dick]

Draw a line connecting the top of the light post to the top of the man's head and continue to where the line hits the ground. There are two similar right triangles. The man is the vertical leg of one and the light post is the vertical leg of the other. The line you drew contains the hypotenuse of both.

 

[Geekchick]

Alright so after I find that, which turns out to be D=9. What am I suppose to do? I don't understand what I am suppose to be finding.

 

[Geekchick]

Never mind I got it. a) 25/3 b) 10/3

Thanks!