Calculate Law of Cosines

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It's an extension of the Pythagorean theorem for non-right triangles.

Use the Law of Cosines when you have either: 1) Two sides and the included angle (SAS case) to find the third side, or 2) Three sides (SSS case) to find the angles.

SAS (Side-Angle-Side) means you know two sides and the angle between them. SSS (Side-Side-Side) means you know all three sides. The calculator handles both cases automatically.

SSA can result in the 'ambiguous case' where there are two possible triangles or no triangle at all. To avoid confusion, this calculator focuses on the unambiguous SAS and SSS cases.

You can use either degrees (default) or radians. The calculator will convert between them automatically. Degrees are more common for most applications.

Besides the sides and angles, the calculator provides the triangle's perimeter, area (using Heron's formula for SSS or trigonometric formula for SAS), inradius, and circumradius.