球面三角法
sin  a 2 = − cos  S cos  ( S − A ) sin  B sin  C cos  a 2 = cos  ( S − B ) sin  ( S − C ) sin  B sin  C tan  a 2 = − cos  S cos  ( S − A ) cos  ( S − B ) cos  ( S − C ) {\displaystyle {\begin{aligned}\sin {\frac {a}{2}}&={\sqrt {\frac {-\cos S\cos(S-A)}{\sin B\sin C}}}\\\cos {\frac {a}{2}}&={\sqrt {\frac {\cos(S-B)\sin(S-C)}{\sin B\sin C}}}\\\tan {\frac {a}{2}}&={\sqrt {\frac {-\cos S\cos(S-A)}{\cos(S-B)\cos(S-C)}}}\end{aligned}}}