Sine Rule, Cosine Rule and Vectors [H]

This lesson covers the sine rule, cosine rule, the area formula using sine, and an introduction to vectors for the Higher tier of AQA GCSE Mathematics. These tools allow you to work with non-right-angled triangles and are essential for the most challenging geometry questions on the paper.

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When to Use Each Rule

graph TD
    A[Non-right-angled triangle] --> B{What do you know?}
    B -->|Two angles and a side| C[Sine Rule]
    B -->|Two sides and the angle between them| D[Cosine Rule to find a side]
    B -->|All three sides| E[Cosine Rule to find an angle]
    B -->|Two sides and the included angle for area| F[Area = half ab sin C]
    B -->|Two sides and a non-included angle| G[Sine Rule but check for ambiguous case]

Exam Tip: The most common mistake is using SOHCAHTOA on a non-right-angled triangle. SOHCAHTOA only works for right-angled triangles. For all other triangles, use the sine rule or cosine rule.

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The Sine Rule

The sine rule relates sides and their opposite angles in any triangle.

a / sin A = b / sin B = c / sin C