What values do I need to solve a triangle?

Any three, except three angles alone (which defines shape but not size). Common cases: SSS (three sides), SAS (two sides + included angle), ASA/AAS (two angles + any side), SSA (two sides + non-included angle — can have 0, 1, or 2 solutions).

What is the Law of Sines?

For any triangle with sides a, b, c opposite angles A, B, C: a/sin(A) = b/sin(B) = c/sin(C). Used when you know an angle-opposite-side pair.

What is the Law of Cosines?

c² = a² + b² − 2ab·cos(C). A generalization of the Pythagorean theorem. Used to find the third side given two sides and the included angle, or any angle given all three sides.

How is the area calculated?

Using Heron's formula when all three sides are known: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2. When two sides and the included angle are known: Area = (1/2)·ab·sin(C).

Triangle Calculator (SSS, SAS, ASA, AAS)

Calculators· 14 tools

Free triangle calculator using the Law of Sines and Law of Cosines. Enter any three values (three sides, two sides + included angle, two angles + one side, etc.) and see all six parameters plus area, perimeter, height, inradius, and circumradius. Handles SSS, SAS, ASA, AAS, and the ambiguous SSA case.

Which values do you know?

Angles in degrees · sides in any unit

Vertex naming: side a is opposite angle A, etc.

∠A36.87°

∠B53.13°

∠C90°

Area6

Perimeter12

Inradius1

Circumradius2.5

h from a4

h from b3

h from c2.4

Frequently Asked Questions

References

Law of Cosines — Weisstein, Eric W. MathWorld — Wolfram MathWorld

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Frequently Asked Questions

References and sources

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