The problem is to find h on this triangle: With the help of the law of sines I've already finished this problem. But I tried doing it a different way and my new solution isn't working and I can't figure out why. Here's what I did: (1) Break the bottom part like so (2) Use tan to solve for x in two ways tan40 = h/x (so x = (tan40)/h) tan47 = h/(125-x) (so x = 125 - hcot47) (3) Since both those equations equal x, they equal each other, so I do this: (tan40)/h = 125 - hcot47 Multiplying both sides by h, blah blah blah, I get this h2cot47 - 125h + tan40 = 0. So I have a quadratic equation in h. When I use the quadratic formula and do all the solving (which I'll omit since it would take a lot of space to write) I get an incorrect answer. Where did I go wrong?