Law of Sines Triangle Solver

The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C) for any triangle, relating each side to the sine of its opposite angle. Given two angles and a side (AAS), the third angle follows from the angle sum (180° − A − B), and the other two sides follow directly from the ratio — this always has exactly one solution.

Given two sides and a non-included angle (SSA) instead — the angle isn't between the two known sides — the same ratio can produce zero, one, or two valid triangles, historically called the 'ambiguous case'. This calculator solves for both possible values of the unknown angle (asin gives an angle and its supplement) and reports every one that actually forms a valid triangle, rather than silently picking just one.

This is a distinct question from this site's triangle-oblique calculator, which solves SSS and SAS triangles via the Law of Cosines — neither of those two 'given' shapes is AAS or SSA, and only the SSA case here can have more than one correct answer for the same input.