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.
The half-side formulas are
- 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.