Law of sines ($\sin A/a=\sin B/b=\sin C/c$)

In a nondegenerate triangle, let $a,b,c$ be the side lengths opposite the interior angles $A,B,C$. Its area $K$ satisfies $2K=bc\sin A=ca\sin B=ab\sin C$. Division by $abc>0$ proves the law of sines. The area formula itself follows by taking the magnitude of the cross product of two edge vectors. Unlike the law of cosines, this relation alone may leave an ambiguity between two supplementary angles when two sides and a nonincluded angle are given.