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GCSE Mathematics · key term
A formula relating all three sides of a triangle to one angle, for example .
Used by AQA, Edexcel and OCR
Specification G22 · Paper 1, Paper 2, Paper 3
Revise: Sine and Cosine RulesThe sine and cosine rules work for any triangle, not just right-angled triangles. Their notation depends on matching each angle to the side directly opposite it.
Specification G22 · Paper 1, Paper 2, Paper 3
A formula relating the three sides of a triangle to one angle, for example .
Revise: Sine and Cosine RulesThe sine rule and cosine rule allow us to solve any triangle, including one with no right angle. To solve a triangle means to find one or more of its unknown side lengths or angles.
Specification 10.05e · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)
A formula relating the three side lengths of any triangle to the cosine of one of its angles: .
Revise: Cosine RuleTwo sides with the angle between them, or all three sides, lead to the cosine rule. A known angle and its opposite side, together with another angle or side, usually lead to the sine rule instead. The ordinary sine, cosine and tangent ratios apply directly to right-angled triangles; they cannot simply be used on an arbitrary non-right-angled triangle.
Use the sine rule only when you know an angle–opposite-side pair. Use the cosine rule for SAS or SSS information.
For the cosine rule, the side on the left must be opposite the angle used in the cosine term.
Use the sine rule only when you have a known opposite side–angle pair. Use the cosine rule for SAS or SSS information.
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