## 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:

whereare the internal angles of the spherical triangle andare the lengths of the sides,being oppositeoppositeandoppositeand S is half the sum of the anglesand