# Related Rates (Right Triangle)

I have a related rates problem that reads as such:

The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s. How long is the ladder?

So from this I'm able to determine: $$a' = -0.15,\quad b' = 0.2,\quad c' = 0,\quad b = 3.$$

How would I go about determining the length of $c$?

I have had some people suggest differentiating the pythagorean theorem, but as far as I can see, that just leaves me either dividing by $0$ (hah) or with the formula $a'a + b'b = 0$. Both are completely useless formulae.

Hint: Your second formula is not useless: from $aa'=-bb'$ you get $a=-bb'/a'$.