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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.

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

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  • $\begingroup$ So if I allow the rate of the hypotenuse to eliminate the hypotenuse from the equation, I can use c = sqrt(((-bb')/a')^2 + b^2) to find the length of c. $\endgroup$ – ciphermagi Oct 23 '15 at 16:48

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