ABC Triangle Solver

Solve all angles and properties of a triangle given its three side lengths (SSS).

Side Lengths

Side a

Side b

Side c

Triangle Analysis

26.83u²

Area

Angle A48.2°

Angle B58.4°

Angle C73.4°

Perimeter24.0

The SSS Case

The SSS (Side-Side-Side) case involves knowing the lengths of all three sides. We can find the area using Heron's formula and calculate all three angles using the Law of Cosines.

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Pro Tips

The Triangle Inequality Theorem requires a + b > c, a + c > b, and b + c > a.
The largest angle is always opposite the longest side.
The sum of the calculated angles should always be 180°.

Fun Facts

"The Law of Cosines is often called the 'generalized Pythagorean theorem'."
"Triangles are the only polygons that are inherently 'rigid'—their shape is fixed entirely by their side lengths."
"The area of a triangle can also be calculated using the sine of any of its angles: Area = 0.5 * b * c * sin(A)."

Formula: cos(A) = (b² + c² - a²) / 2bc

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