Here's a problem that's been bugging me. A student asked me this a couple of days ago and I just can't get out of the circles it's twisting.

(See diagram below.)

I can't seem to find a way to reduce the possible equations to something with one dependent variable. (This is supposed to be a Calc I problem.) Any takers?A 15 ft ladder is constrained to keep one point on the ground. The ladder is propped up by a vertical 8 ft support that can be moved back and forth. What is the maximum horizontal extension of the ladder? (Marked as the line y in the diagram.)

-Dan