Spherical Triangles and The Half Side Formulae
For a triangle drawn on the surface of a sphere, the internal angles do not sum to 180, nor do the ordinary sin rule, cosine rule or Pythagoras theorem apply. Instead we use the half side formulae:
where
are the internal angles of the spherical triangle and
are the lengths of the sides,
being opposite
opposite
and
opposite
and S is half the sum of the angles
and