SOLUTION: A spherical triangle on a sphere has an area of 419 sq.m. Find the radius of the sphere if the spherical excess of the triangle is 60 degrees.

On a sphere of a radius R, the spherical area of a triangle 


Spherical Area = ,


where A, B and C are spherical angles of the triangle in radians and the value    is called  

"the spherical excess of the triangle"  (see the link  http://mathworld.wolfram.com/SphericalTriangle.html ).


So, from the given data,   =  =  = 400.3185.


Therefore, the radius of the sphere is about   = 20 meters.