There are two poles (lets say poles A and B) $50$ feet apart and the poles are $15$ and $30$ feet tall. There is a wire which runs from the top of pole A to the ground, and then to the top of pole B so that two triangles are made. What is the minimum length of wire needed to set up this configuration?
I tried finding this by setting up an equation for the length of the wire and taking the first derivative, but I ended up with an ugly polynomial.
I also tried drawing in one more triangle and used the law of cosines, but that didn't turn out too well either.
The most likely source of this problem (altough it had different numbers) is from "Maxima and Minima Witouth Calculus" by Ivan Niven, but I'm not sure.