△ Trigonometry

Law of Cosines

Find a side when two sides and included angle known

Formula

c² = a² + b² − 2ab cos C

Find a side when two sides and included angle known

Example

  • a=5, b=7, C=60°
  • c² = 25+49−70×0.5 = 39
  • c ≈ 6.24
Result ≈ 6.24
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Updated July 2026

FAQs

What is Law of Cosines?

Law of Cosines (law of cosines) is a trigonometry relationship written as Find a side when two sides and included angle known or c² = a² + b² − 2ab cos C. Students use it to solve unknowns when enough values are known.

How do you calculate Law of Cosines step by step?

Write Find a side when two sides and included angle known, substitute the known numbers carefully, then simplify. Worked walkthrough: a=5, b=7, C=60° c² = 25+49−70×0.5 = 39 c ≈ 6.24.

When is Law of Cosines taught in school?

Law of Cosines usually appears in trigonometry units during middle or secondary school. Match difficulty with MathDigits grade worksheets so practice fits the curriculum year.

What is a real example of Law of Cosines?

On this page the worked result is ≈ 6.24. Generate a formula worksheet below for more unique practice sets.