Triangle Solver Calculator (SSS, ASA, AAS, SAS, SSA) | Law of Sines & Cosines

Triangle Solver (SSS, SAS, ASA, AAS)

High School Triangle Solver

Solve any triangle using SSS, SAS, ASA, or AAS methods and visualize the result.

Sides

Side a
Side b
Side c

Angles (Degrees)

Angle A
Angle B
Angle C

Properties

Area: Perimeter:

Triangle Solver Visualization

About the Triangle Solver

Trigonometry is the branch of mathematics dealing with the relationships between the sides and angles of triangles. While right-angled triangles are simple to solve using Pythagoras, oblique (non-right) triangles require more advanced laws. This tool automates those calculations.

Solving Methods

  • SSS (Side-Side-Side): You know the lengths of all three sides. We use the Law of Cosines to find the angles. Note: The sum of any two sides must be greater than the third side for a valid triangle.
  • SAS (Side-Angle-Side): You know two sides and the included angle between them. We use the Law of Cosines to find the third side, then the Law of Sines for the remaining angles.
  • ASA (Angle-Side-Angle): You know two angles and the side connecting them. Since angles in a triangle sum to 180°, finding the third angle is simple arithmetic. The Law of Sines finds the remaining sides.
  • AAS (Angle-Angle-Side): Similar to ASA, but the known side is not between the angles. We find the third angle first, then use the Law of Sines.

Important Formulas

Law of Sines: a/sinA = b/sinB = c/sinC
Law of Cosines: c² = a² + b² – 2ab cos(C)

FAQ

Is this Triangle Solver free?

Yes, this tool is completely free for students and educators.

What is the “Ambiguous Case”?

This happens in SSA (Side-Side-Angle), which this tool simplifies. Sometimes two different triangles can be formed with the same measurements. This solver calculates the primary acute solution.

Does the Triangle Solver check for validity?

Yes. If you enter sides 1, 1, and 100, it will tell you that no such triangle exists because the sides don’t connect.

Are angles in degrees or radians?

This calculator uses Degrees for all angle inputs and outputs.

HIGHER SCHOOL