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Cosine Rule - GCSE Maths Definition

Reviewed by: Dan Finlay

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The Cosine Rule is a formula used in trigonometry to find missing sides or angles in any triangle, not just right-angled ones. It is particularly useful when you know two sides of a triangle and the angle between them, or when you know all three sides but want to find an angle.

Non Right-Angled Triangle labelled with angles A, B and C and opposite corresponding sides a, b and c.

The Cosine Rule states that in any triangle:

c squared space space equals a to the power of 2 space end exponent space plus b squared space space minus 2 a b cos C

where:

  • c is the side opposite to angle C,

  • a and b are the other two sides, and

  • C is the included angle between sides a and b.

By rearranging the formula, you can also find an angle if you know all three sides. The Cosine Rule helps solve problems involving triangles in a straightforward way and is an important part of the GCSE Maths curriculum.

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Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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