球面三角法
sin  a cos  B = cos  b sin  c − sin  b cos  c cos  A sin  a cos  C = cos  c sin  b − sin  c cos  b cos  A {\displaystyle {\begin{aligned}\sin a\cos B&=\cos b\sin c-\sin b\cos c\cos A\\\sin a\cos C&=\cos c\sin b-\sin c\cos b\cos A\end{aligned}}}
球面三角法の正接定理
tan  A + B 2 tan  A − B 2 = tan  a + b 2 tan  a − b 2 {\displaystyle {\frac {\tan {\dfrac {A+B}{2}}}{\tan {\dfrac {A-B}{2}}}}={\frac {\tan {\dfrac {a+b}{2}}}{\tan {\dfrac {a-b}{2}}}}}
球面三角法の余接定理
cot  a sin  b = cos  b cos  C + cot  A sin  C {\displaystyle \cot a\sin b=\cos b\cos C+\cot A\sin C}
面積(球面の半径 = r {\displaystyle =r} ,球過量 (Spherical Excess) = E {\displaystyle =E} , 2 s = a + b + c {\displaystyle 2s=a+b+c} )
球面三角形ABCの面積 = E r 2 {\displaystyle =Er^{2}}