Ok, after some more digging through the internet I think I managed to find the solution:
Everyone thanks for reading and thinking about this nevertheless!
This is not a homework problem, it's part of a practial engineering problem that I'm trying to solve. I have been struggling with it for a few hours already. I know I should use the Napier rules, but somehow I can't figure it out yet.
I've got a right spherical triangle in which angle A and side c are known. What is the formula for side b?