Take into account, for instance, that the laws of sine and cosine are given by:
the previous expressions represent the use of the laws only for certain cases.
You can notice that the law of cosine can be used when you have information about two sides of the triangle and one angle (if you have information about the three sides you can find a missing angle).
The law of sine can be used when you have information about two interior angles and one side.
Then, based on the previous description, you can conclude for the given triangles that the law you shiuld use is:
28) In this case, you can use law of cosines to solve for one of the interior angles.
29) Law of sines, because you have information about two interior angles.
30) Law of cosine, to find the value of the missing leg.
31) Law of sine, to find the value of a missing leg.