How to Calculate Angles in a Triangle Using the Cosine Rule

Learn to find angles in triangles when you know all sides using the cosine rule.

96 views

To find an angle if you know all sides of a triangle, use the cosine rule: cos(C) = (a² + b² - c²) / (2ab). Here, a, b, and c are the lengths of the sides, and C is the angle opposite side c. Rearrange to solve for C: C = arccos[(a² + b² - c²) / (2ab)]. Apply this formula to calculate any angle when the sides are known.

FAQs & Answers

  1. What is the cosine rule used for? The cosine rule is used to find unknown angles or sides in a triangle when the lengths of all three sides are known.
  2. Can you use the cosine rule for non-right triangles? Yes, the cosine rule is applicable for all types of triangles, not just right triangles.
  3. How do you rearrange the cosine rule to find an angle? To find an angle using the cosine rule, rearrange the formula to isolate the angle variable and apply the arccos function.
  4. What do a, b, and c represent in the cosine rule? In the cosine rule, a and b are the lengths of two sides of the triangle, while c is the length of the side opposite the angle you want to find.