Let us consider skew-angled triangles. If one knows three parts of a triangle, among which at least one side, then the other parts may be calculated by using the law of sines and the law of cosines. We distinguish four cases:

1. ASA. Known two angles and one side, e.g. , , . Other parts:
   

   Figure: ASA (angle-side-angle)

2. SSS. Known all sides , , . The angles are obtained from
   

   Figure: SSS (side-side-side)

3. SAS. Known two sides and the angle between them, e.g. , , . Other parts from
   

   Figure: SAS (side-angle-side)

4. SSA. Known two sides and the angle opposite of one of them, e.g. , , . Other parts are gotten from
   

   Figure: SSA (side-side-angle)

   Since the SSA criterion alone does not prove congruence, it is not surprising that there may not always be a single solution for here. In fact, if the first equation gives , then the situation is impossible and the triangle does not exist. If the equation gives , one gets two distinct values of ; an acute and an obtuse . If in this case , then there are two different triangles as solutions, but if , then there is only one triangle.

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