If the sides of the triangle are A, B and C and the angles opposite to those sides are a, b and c, respectively, then the law of sines states that: .
Let a, b, and c be the sides of a triangle opposite the angles A, B and C to side b, perpendicular to each other. This divides the original triangle into two right triangles. We let X be the length of this dividing line.
Since sine is opposite divided by hypotenuse, then
Solving for X in the first two equations,
By cross products,
But solving for a,
Combining the resulting equations, we get