Law of Sines

Relates sides to the sines of their opposite angles in any triangle.

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

Variables

Use it when you know two angles and a side (ASA/AAS) or two sides and a non-included angle (SSA — watch for the ambiguous case).

$A = 30°, C = 90°, c = 10$ : $a = 10 sin 30° = 5$ .

Solve any triangle from SSS, SAS or ASA: all sides, angles, area, perimeter and type using the laws of sines and cosines.

Law of Cosines

Generalizes the Pythagorean theorem to all triangles.