 Law of sines

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.

The Law of Sines is a fundamental relation in trigonometry that relates the angles and sides of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.