The problem is to find h on this triangle:(adsbygoogle = window.adsbygoogle || []).push({});

http://img215.imageshack.us/img215/7006/triangleum3.png [Broken]

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

http://img221.imageshack.us/img221/3079/bottomba3.png [Broken]

(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

h^{2}cot47 - 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?

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# Homework Help: Finding the height of this triangle

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