Law of Sines explained
The law of sines says that each side divided by the sine of its opposite angle is the same ratio: a/sin(A) = b/sin(B) = c/sin(C). It is most useful when you know two angles and one side, or in the SSA ambiguous case.
Law of Cosines explained
The law of cosines extends Pythagoras to any triangle: c² = a² + b² - 2ab cos(C). It is the standard route for SSS and SAS problems.
The ambiguous SSA case
SSA can produce zero, one, or two valid triangles because the known angle is not between the two known sides. When two solutions exist, this calculator shows both possible triangles separately.