Triangle Solver

Solve any triangle for its missing sides and angles using the law of sines and the law of cosines, with the case identified (SAS, ASA, SSS, SSA). Try “solve triangle with a = 8, b = 11, C = 40°”.

Try an example:

What you can do with the Triangle Solver

Law of sines, law of cosines, angles and sides.

Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.

Example input

e.g. solve triangle with a = 8, b = 11, C = 40 degrees

How the Triangle Solver works

  1. Work out which case you have from the given sides and angles.
  2. Use the law of cosines for SAS or SSS, and the law of sines for ASA, AAS or SSA.
  3. Use the angle sum of 180° to get the last angle, then check the largest angle faces the longest side.

Frequently asked questions

When do I use the law of sines vs cosines?

Use cosines when you know two sides and the included angle (SAS) or all three sides. Use sines when you have a side and its opposite angle.

What is the ambiguous case?

With two sides and a non-included angle (SSA) there can be zero, one or two valid triangles.

More Geometry & Trigonometry calculators

Geometry CalculatorArea and perimeter of triangles, rectangles, circles and polygons. Volume & Surface AreaCubes, cylinders, cones, spheres and prisms. Pythagorean TheoremFind a missing side of a right triangle. Circle CalculatorCircumference, arc, sector, chord and tangent problems. Angles & Parallel LinesAngle sums, polygons, parallel-line and triangle angle rules. Coordinate GeometryDistance, midpoint, slope and equation of a line.

Browse all calculators →

Math Solver can make mistakes. Please double-check important steps and calculations.