Cosine rule

Definition

The cosine rule relates all three sides of any triangle to one angle. Use it when you know three sides, or two sides and the included angle.

Worked example

With b = 7, c = 9 and A = 60°: a² = 49 + 81 − 2(7)(9)cos60° = 67, so a ≈ 8,19.

Where it appears in the exam

Paper 2 uses the cosine rule in 2D and 3D trigonometry problems, often together with the sine rule and the area rule.

Step-by-step method

1. Label the triangle so the unknown side is opposite the known angle.
2. Write a² = b² + c² − 2bc·cosA.
3. Substitute and calculate.
4. Take the square root for a side, or rearrange for cosA to find an angle.

Common mistake

Working out b² + c² − 2bc first and then multiplying by cosA, ignoring the order of operations.

Related trigonometry terms

• Reduction formula
• General solution

Frequently asked questions

What does cosine rule mean in Grade 12 Maths?

The cosine rule relates all three sides of any triangle to one angle. Use it when you know three sides, or two sides and the included angle.

Which NSC paper tests cosine rule?

Cosine rule belongs to the Trigonometry section of CAPS Grade 12 Mathematics, which is examined in Paper 2.

How do I practise questions involving cosine rule?

Snap a question that uses cosine rule into the Snap&Learn AI solver, or work through the trigonometry topic guide and NSC past papers.