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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.

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

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.

Law of Cosines 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