Law of sines calculator

Solve triangles using a/sin(A) = b/sin(B). Enter an angle, its opposite side, and one other known value.

Angle A (°) Side a

Angle B (°)

Law of sines formula

a/sin(A) = b/sin(B) = c/sin(C)

This ratio is the same for all three side-angle pairs in any triangle.

When to use law of sines

AAS (angle-angle-side): Two angles and a non-included side → find everything else.

ASA (angle-side-angle): Two angles and the included side → find everything else.

SSA (side-side-angle): Two sides and a non-included angle → ambiguous case (may have 0, 1, or 2 solutions).

The ambiguous case (SSA)

When given two sides and an angle opposite one of them, there may be no triangle, one triangle, or two triangles. This calculator checks all possibilities and shows all valid solutions.