Solve any triangle from SSS, SAS, ASA, or AAS — every side, angle, and step shown, drawn to scale.
Choose the case that matches what you know: three sides (SSS), two sides and the included angle (SAS), or two angles and a side (ASA or AAS). The solver finds everything else.
The law of cosines, cos A = (b² + c² − a²) / 2bc, turns three side lengths into angles. The solver first checks the triangle inequality: each side has to be shorter than the other two combined, or no triangle exists.
With two sides and the angle between them, the law of cosines gives the third side, a² = b² + c² − 2bc·cos A. The remaining angles follow from the law of cosines again, and they always add up to 180°.
Two angles fix the third, since the angles sum to 180°. The law of sines, a/sin A = b/sin B = c/sin C, then scales the known side to the other two. Area comes from Heron's formula or ½ab·sin C.