**SSS**: When you input all three sides, the calculator uses the law of cosines to find each of the angles.
**SAS:** When you input two sides and the included angle (notice "A" is between each "S") the calculator first uses the law of cosines to find the third side, and then uses the law of sines and triangle sum theorem to find the remaining angles.
The next case is the most challenging:
**SSA**: When you input two sides and a non-included angle you are dealing with the "ambiguous case." The calculator will indicate whether there is no possible triangle, or if there are two different cases. Once it identifies which case your triangle is, it will use the law of cosines to find the last side, then the law of sines to find the two unknown angles.
**AAS:** When you input two angles and the non-included side, the calculator first finds the third angle using the triangle sum theorem, and then uses the law of sines to find the unknown sides.
**ASA**: When you input two angles and the included side, the calculator first finds the third angle using the triangle sum theorem, and then uses the law of sines to find the unknown sides.
**AAA**: When you input all three angles, the calculator performs no action. This is because the size of a triangle cannot be determined without at least one side. You can find the shape, but not the size.
Try drawing 2 different equilateral (and equiangular) triangle where all the angles are 60 degrees. |