From "side-side-angel", is other angle obtruse or acute in triangle?

Wikipedia has a great article about solving triangles, here's a link to my problem, se in particular:

-point 3) D<1

--subpoint 1) b<c

Solution of triangles - Wikipedia, the free encyclopedia

I know two sides and a non-included angle in a triangle.

If the known angle is not obtruse, it seems one cannot determine which of (if any) of the remaining two angles is obtruse. Therefor there are two solutions.

I have a specific problem where this changes from time to time, as a apart of a bigger geometric context. So I could look for ways to test which of the solutions is consistent with other measurements I have in the bigger geometric context (not yet clear about how, though). I'm looking for general advice for such an approach. Or if there's some smarter way out.

http://upload.wikimedia.org/wikipedi..._solutions.png

Blue known