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Toolkit 58

Law of Cosines

Triangle ABC with sides a, b, c

For a triangle with sides aaa, bbb, ccc:

a2=b2+c2−2bccos⁡Aa^2=b^2+c^2-2bc\cos Aa2=b2+c2−2bccosA

or

cos⁡A=b2+c2−a22bc\cos A=\frac{b^2+c^2-a^2}{2bc}cosA=2bcb2+c2−a2​

Related Problems

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Major

  • AMC 12A 2025 (Problem 24)
  • AMC 12B 2025 (Problem 21)
  • AMC 12B 2025 (Problem 25)
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