How to Calculate an Angle in a Non-Right Triangle Using the Law of Cosines

Learn how to find an angle in a non-right triangle with the Law of Cosines formula.

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To find an angle if you have two sides of a non-right triangle, use the Law of Cosines. The formula is: cos(C) = (a² + b² - c²) / (2ab), where C is the angle, and a, b, and c are the sides of the triangle. Solve for C to find the angle.

FAQs & Answers

  1. What is the Law of Cosines used for? The Law of Cosines is used to find an unknown side or angle in any triangle when provided with sufficient information.
  2. Can the Law of Cosines be used for right triangles? Yes, the Law of Cosines can be used for right triangles, but simpler methods like the Pythagorean theorem are often preferred.
  3. How do I solve for an angle using the Law of Cosines? Rearrange the formula cos(C) = (a² + b² - c²) / (2ab) to isolate C, then use the inverse cosine function to find the angle.
  4. What if I have only one side and one angle? With only one side and one angle, additional information is required, as the Law of Cosines needs at least two sides and the included angle or all three sides.

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