What type of problems can always be solved using the law of cosines or sines?

Anytime you have a triangle (right triangles are preferred) where at least 2 angle measures and 1 side is known. Or, at least two sides and 1 angle measure.

OR ... 3 sides or three angles are known. So, sines or cosines could be used at almost anytime to find the sides and angles of a triangle!