Certified calculator · Version 1

Triangle Calculator

Enter three valid side lengths to calculate area, perimeter and all three interior angles deterministically.

Side aSide bSide c

Area6

Perimeter12

Angle A36.8698976458°

Angle B53.1301023542°

Angle C90°

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Goal SolverSolve backwards from the outcome you want.

Result methodology

Heron's formula and the law of cosines from the same validated side lengths.

Solution steps

s = (a+b+c)/2 = 6
Area = √(s(s-a)(s-b)(s-c)) = 5.999999999999998
Angles = 36.86989764584401°, 53.130102354155994°, 89.99999999999999°

How this calculator works

Heron's formula gives the area from the semiperimeter, while the law of cosines determines the angles.

Formula

K=√(s(s-a)(s-b)(s-c)); cos A=(b²+c²-a²)/(2bc)

Uses Heron's formula and the law of cosines for a valid SSS triangle.

Worked example

3-4-5 triangle is a verified test case used by the calculation engine.

Assumptions and limitations

All side lengths are positive.
The three sides must satisfy the triangle inequality.
Angles are reported in degrees.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

CalcuMint deterministic geometry engine

Frequently asked questions

What inputs are required?

Three side lengths that form a valid triangle.

How is the area calculated?

Area is calculated with a numerically scaled form of Heron’s formula.