Question

list two congruence conditions for the law of sines yields a unique solution

Answer 1

Your question makes no grammatic sense. The law of sines is valid for any triable, and has nothing to do with conguence. Congruence conditions apply to pairs of triangles, and are:
side/side/side
side/angle/side
angle/side/angle
angle/side/side (ambiguous case)

See
http://en.wikipedia.org/wiki/Congruence_(geometry)