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.
- a, b, c are the lengths of the sides respectively opposite angles A, B, C,
- is half the sum of the angles, and
The three formulas are really the same formula, with the names of the variables permuted.
To generalize to a sphere of arbitrary radius r, the lengths a,b,c must be replaced with
so that a,b,c all have length scales, instead of angular scales.