Trigonometry, knowing 3 sides how to find the height? I have a mathematician problem where, I knew the 3 sides of a triangle, with these sides I can figer out what type of type of triangle is.
What I realy want to find is the height of the triangle and another one "side".

Let me explain what I want, with the above picture. 
I knew a,b and c and I can calculate the 2 angles (the angle oposite of C, and the angle oposite of b, those on the black dots). I want to find out the red dots (the bottom red dot is is the other "side" I note before, from black dot to red dot distance).
So I want to to know the (x,y) for the red dot at the top, via the combination of height length, b OR c length (which also needs the two angles) in case to find the absolute right (x,y) for the red dot at the top.
Thanks.

Or from Heron's formula for triangle area http://en.wikipedia.org/wiki/Heron%27s_formula
