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Trigonometric Law of Cosines Angle Calculator

Find an angle from all three triangle side lengths using the law of cosines.

Angle C (degrees): -
Visual representation

Trigonometric Law of Cosines Angle 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 side lengths must be positive and satisfy the triangle inequality. Floating-point inputs near a degenerate triangle can be sensitive.
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How the Trigonometric Law of Cosines Angle Calculator works

Find an angle from all three triangle side lengths using the law of cosines.

Formula

arccos((sideA × sideA+sideB × sideB-sideC × sideC) ÷ (2 × sideA × sideB)) × 180 ÷ π

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 side lengths must be positive and satisfy the triangle inequality. Floating-point inputs near a degenerate triangle can be sensitive. Decimal answers are rounded for display; retain additional precision for subsequent calculations.

Geometry collection

This calculator belongs to the Trigonometry section of the Math calculator library.

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