Study Notes
The Cosine Rule is used to calculate unknown sides and angles in triangles that are not right-angled. It is applicable when given two sides and the included angle (SAS) or all three sides (SSS).
- Cosine Rule — the square of the length of any side of a triangle equals the sum of the squares of the lengths of the other sides minus twice their product multiplied by the cosine of their included angle. Example: For triangle ABC, c² = a² + b² - 2ab * cos(C).
Exam Tips
Key Definitions to Remember
- The Cosine Rule formula: c² = a² + b² - 2ab * cos(C)
Common Confusions
- Confusing when to use the cosine rule versus the sine rule
- Forgetting to use the cosine of the included angle
Typical Exam Questions
- Given two sides and an included angle, find the third side? Use the cosine rule to calculate the unknown side.
- Given all three sides, find an angle? Use the rearranged cosine rule to find the angle.
- How to combine the cosine and sine rules in a problem? Use the cosine rule first to find a side or angle, then apply the sine rule if needed.
What Examiners Usually Test
- Ability to correctly apply the cosine rule in SAS and SSS cases
- Understanding of when to use the cosine rule versus the sine rule