How do you use the Law of Cosines and Sines in various ambiguous cases?
First of all, there are not ambiguous cases.
To solve a triangle it is necessary to know at least three elements (except the case the three elements are the three angles, in that case the triangle is not unique).
It is mandatory to use the Law of Cosine in only one case: if two sides and their enclosed angle are known. In all other cases it is mandatory to use Law of Sines.
In the cases, in which are known more than three elements, it is always preferable to use, if it is possible, the Law of Sines because the functions, in these Laws, are all linear and not quadratic .