Every spherical triangle on a unit sphere (sphere with radius 1) is uniquely defined by any 3 of the following angles that are either its sides a, b and c, or angles A, B and C between two sides meeting at vertex the A, B or C respectively. By specifying any 3 independent angles of a particular spherical triangle, we calculate and determine all of the other angles. Finally, if you specify the different value for the radius R of the sphere, or you specify the arc lengths of any of the triangle sides, we will calculate all other arc lengths for other sides and radius of the sphere. Please note:
If you provide more then 3 elements of the triangle, only 3 from the provided ones will be used for the construction of the triangle. They will be selected in the following order of preference: angles, then sides and finally arc lengths.
If you specify 2 sides and an angle not between them, lets say b, c and B, then the solution exists only if b > arcsin( sin(c) sin(B) ) . If that condition holds, and if b<c (the side b opposite the angle B is shorter than the other side c), than there are two solutions based on C and π - C.
If you specify one side and one angle adjacent to it and one opposite it, lets say a, A and B, then if the angle for the side a is acute and A > B, then there are two solutions based on b and π - b.
All values are calculated with the precision of 10-15, but are displayed with the precision of 10-9.
