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.
For a triangle 
where a, b, c are the angular lengths (measure of central angle, arc lengths normalized to a sphere of unit radius) of the sides opposite angles A, B, C respectively, and 
The polar dual relationship for a spherical triangle is the half-angle formula,
where semiperimeter 
Half-tangent variant
The same relationships can be written as rational equations of half-tangents (tangents of half-angles). If 
and the half-angle formula is equivalent to:
