# There are four cases in which solutions to oblique triangles can be classified

There are four cases in which solutions to oblique triangles can be classified. (1) two angles and one side – AAS, (2) two sides and a non-included angle – SSA, (3) three sides – SSS, (4) two sides and their included angle – SAS.
Looking at the first case, when given two angles and one side of a triangle, you will use the Law of Sines to solve. The next case is known as the ambiguous case. It is slightly more complicated because it includes the possibility of more than one triangle being formed (or none at all). When given two sides and a non-included angle, or SSA case, the Law of Sines is used. To solve you have to first determine how many possible triangles exist. Then, based on that, you can use the Law of Sines to find the missing values.
The next two cases, SSS and SAS, are going to be solved using the Law of Cosines. When given values for all three sides or two sides and their included angle, it is not possible to solve using the Law of Sines because the given information can’t produce complete ratios using that formula. Thus, the Law of Cosines must be used in order to find a solution.

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