球体的正弦定律

It turns out that there is a nice version of the law of sines for spherical triangles too! Let $ABC$ be a spherical triangle with spherical side lengths $a,b,c$ opposite spherical angles $A,B,C$. Then $$\frac{\sin A}{\sin a}=\frac{\sin B}{\sin b}=\frac{\sin C}{\sin c}.$$

For a derivation, see here.