Well, the reason I used the crazy substitution for x is...I guess I thought that since y=sqrt 15^2-x^2 then x would be sqrt15^2-y^2 or sqrt15^2-x^2. I still haven't absorbed your psot so I don't know exactly the why of it. I will work with it later in the day. As for using the Pythagorean theorem, wouldn't that have been assured by telling us that the triangle is a right triangle? Why would we need to know that the figure had been inscribed in a semicircle?

The semicircle is WHY you can know it's a right triangle. The problem itself only

*stated* the former; the HINT represents what you have to deduce

*from* that. It shouldn't have been given, in my opinion, because it makes the problem too easy by not making you realize that yourself.

I imagine the reason you did the unnecessary substitution was mere momentum! You did that for y, so you did it for x as well. It wasn't wrong; it just took you past your goal so you had to stop, think, and back up. (Yes, I'm picturing the "momentum" literally.)