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Trigonometry Calculators

Law of Cosines Calculator

Find the third side of a triangle from two sides and the included angle (SAS) with the law of cosines, plus the remaining angles.

Enter values

Results update as you type.

Result

Side c

7.00062577

Angle A
49.9939 °
Angle B
80.0061 °
Area
24.1304
Step-by-stepShow
  1. c² = 7² + 9² − 2·7·9·cos 50° = 49.008761

About the Law of Cosines Calculator

Find the third side of a triangle from two sides and the included angle (SAS) with the law of cosines, plus the remaining angles.

Also known as: cosine rule, sas triangle, law of cosines formula.

How to use this calculator

  1. Enter side a, side b, included angle c.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Open “Step-by-step” to see how the answer was worked out.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

c² = a² + b² − 2ab·cos C

Worked example

Using the values pre-filled in the calculator above:

  • Side a = 7
  • Side b = 9
  • Included angle C = 50 °

the calculator returns:

  • Side c: 7.00062577
  • Angle A: 49.9939 °
  • Angle B: 80.0061 °
  • Area: 24.1304

Working

  1. c² = 7² + 9² − 2·7·9·cos 50° = 49.008761