law of sines

law of sines, principle of trigonometry stating that the lengths of the sides of any triangle are proportional to the sines of the opposite angles. That is, $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$when a, b, and c are the sides and A, B, and C are the opposite angles. The law of sines is used when one knows the lengths of two sides and an opposite angle to one of those sides to calculate the other opposite angle or when one knows two angles and the length of one of the opposite sides to calculate the length of the other opposite side.

There is a similar law of sines for triangles on a sphere; that is, $\frac{\sin a}{\sin A}=\frac{\sin b}{\sin B}=\frac{\sin c}{\sin C}$, where a, b, and c are the sides of the spherical triangle as measured by the angles subtended from the center of the sphere, and A, B, and C are the angles opposite those sides on the spherical triangle.