Trigonometry

These pages solve plane triangles. Each tool asks for sides and angles, then shows the formula with your numbers filled in.

Order of work

If one angle is 90°, open the right triangle calculator.
If you have two angles and a side, or SSA, open the law of sines.
If you have SAS or three sides, open the law of cosines, then the area calculator if you need the area.

A longer explanation is in the method guide.

The calculator finishes AAS, ASA, and SSA, and it names the ambiguous case when two triangles fit the data.

The calculator finds a missing side from SAS or a missing angle from three sides.

The calculator returns the third interior angle from A + B + C = 180°.

The calculator uses the Pythagorean theorem and the sine, cosine, and tangent ratios when one angle is 90°.

The calculator finds the area from two sides and the included angle, or from three sides.

A written map from AAS, SAS, SSS, SSA, and a right angle to the matching calculator.

A written guide for the height test that decides whether SSA gives zero, one, or two triangles.