The Law of Sines

In any triangle, each side is proportional to the sine of its opposite angle: a/sin A = b/sin B = c/sin C. This law of sines calculator uses that constant ratio to complete a triangle from two angles and one side, or from two sides and a non-included angle.

AAS and ASA

Knowing two angles fixes the third at 180° minus their sum, and any one side then scales the entire triangle through the sine ratio. These two configurations always produce exactly one solution.

The Ambiguous SSA Case

Two sides and a non-included angle can describe zero, one, or two triangles. The calculator detects all three: no solution when the known side falls short of the altitude, one solution at or beyond the critical length, and two solutions in between — with both reported in the results.