Half-side formula
In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.
Formulas
![\begin{align}
\tan\left(\frac{a}{2}\right) & = R \cos (S- \alpha) \\[8pt]
\tan \left(\frac{b}{2}\right) & = R \cos (S- \beta) \\[8pt]
\tan \left(\frac{c}{2}\right) & = R \cos (S - \gamma)
\end{align}](/2012-wikipedia_en_all_nopic_01_2012/I/5d4594755dff6fdc7bb707877a12a2f6.png)
where
- a, b, c are the lengths of the sides respectively opposite α, β, γ,
is half the sum of the angles, and
The three formulas are really the same formula, with the names of the variables permuted.