What is the geometrical meaning of the common value in the law of sines, $\frac{\sin A}{\sinh a} = \frac{\sin B}{\sinh b} = \frac{\sin C}{\sinh c}$ in hyperbolic geometry? I know the meaning of this value only in Euclidean and spherical geometry.

EDIT, Will Jagy. The OP is looking for some fourth fairly natural real number that can be calculated from a triangle, that gives the same answer as the common value in the Law of Sines. The original question is at http://math.stackexchange.com/questions/69345/the-law-of-sines-in-hyperbolic-geometry

notcall something a constant when it depends on the triangle chosen. – Will Jagy Oct 4 '11 at 20:32