If I have a triangle and vertices are a, b, and c, and I know the angle of a and b, and the distance between a and b, what formula can I use to find the height? No angle will necessarily be 90 degrees.
It's actually pretty easy, here we go:
You have angles A & B, and the distance between them is AB or a, this case is calledAngle- Side-Angle)
Find angle C = 180 - (A + B)
Find sides AC = b , BC = a, using the sine rule:
a/sinA = b/sinB = c/sinC
Edit: Re: the height: let h = the height AH drawn form A to BC, then:
sinC = h/b => h = sinC * b
Law of Cosines
This is like the Pythagorean Theorem for non-right triangles.