The Cosine Rule

The cosine rule relates one angle and three sides of any triangle.

Hence, use the cosine rule for questions involving 3 sides and 1 angle (one of which you’re trying to find!)

Alternatively, use the sine rule for questions involving 2 sides and 2 angles (one of which you’re trying to find!)

Side ‘c’ is the side opposite the given angle/the angle you are trying to find.

Angle ‘C’ is the angle opposite the side you’re trying to find.

Finding Sides

Rule: c2=a2+b2−2abcos⁡Cc^2=a^2+b^2-2ab\cos C

Slightly Rearranged: c=a2+b2−2abcos⁡Cc=\sqrt{a^2+b^2-2ab\cos C}

Finding Angles

Rule: cos⁡C=a2+b2−c22ab\cos C=\frac{a^2+b^2-c^2}{2ab}

Slightly Rearranged: CC=cos⁡−1(a2+b2−c22ab)C=\cos^{-1}\left(\frac{a^2+b^2-c^2}{2ab}\right)