Which of these problem types can not be solved using the law of sines? a. aas b. asa c. aaa d. sas

I suppose what is meant is given triangles with known sides or angles, which combination cannot be completely solved by the law of sines.

To start, law of sines can only solve problems with at least one angle and the opposite side known.
1. AAS means we know all three angles, since two of the three angles are known, and therefore we will certainly know one side and the opposite angle, so yes, it can be solved by the rule of sines.
2. see 1 above
3. SSS does not provide any know angle, so law of sines is useless.  Use cosine rule.
4. SAS provides two known sides and the INCLUDED angle, so there is no side with opposite angle known.  Cosine rule should be used.  Sine rule will not work.