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Law of Cosines Side Calculator

Find the third side of a triangle from two sides and their included angle.

Side c: -
Visual representation

Law of Cosines Side Calculator diagram

The diagram updates with your entries and is illustrative, not necessarily drawn to scale.

Calculation explained

How this result was calculated

The formula, your substituted values, and the evaluated result are shown below.

The included angle must be greater than 0° and less than 180°. The radicand must be non-negative.
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How the Law of Cosines Side Calculator works

Find the third side of a triangle from two sides and their included angle.

Formula

√(sideA × sideA+sideB × sideB-2 × sideA × sideB × cos(angleC × π ÷ 180))

How to use this calculator

  1. Enter every measurement using one consistent length or angle unit.
  2. Select Calculate to evaluate the formula.
  3. Review the substituted values in the calculation explanation.

Interpretation and limitations

The included angle must be greater than 0° and less than 180°. The radicand must be non-negative. Decimal answers are rounded for display; retain additional precision for subsequent calculations.

Geometry collection

This calculator belongs to the Plane Geometry section of the Math calculator library.

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