When does SSA (two sides and a non-included angle) fail?

SSA can give zero, one or two triangles (the ambiguous case), which is why this calculator uses SSS, SAS and ASA.

Triangle Calculator

Solve a triangle completely from three known values. The calculator uses the law of cosines, the law of sines and Heron's formula, and classifies the triangle.

How to use the triangle calculator

Choose which values you know.
Enter them (angles in degrees).
Get all sides, angles, area and perimeter.

Examples

SSS 3, 4, 5

Answer: Right triangle, area 6

Formulas

Heron's Formula

A = s (s - a) (s - b) (s - c), s = \frac{a + b + c}{2}

Law of Cosines

c^{2} = a^{2} + b^{2} - 2 ab cos C

Law of Sines

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}