 # Cosine Rules

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What is the Sine Rule?

For sides, $$\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}}$$

For angles, $$\frac{{\sin A}}{a} = \frac{{\sin B}}{b} = \frac{{\sin C}}{c}$$

What is the Cosine Rule?

To find a side when you know the other two sides and the angle between them use:
$${a^2} = {b^2} + {c^2} - 2bc\cos A$$

To find an angle when you know three sides use:
$$\cos A = \frac{{{b^2} + {c^2} - {a^2}}}{{2bc}}$$

Sine and Cosine Rule
Sine and Cosine Rule - Exam Questions

Cosine rule (Finding a Length)
How to find the length of a side of a triangle using the cosine rule?
Cosine rule (Finding an Angle)
How to find an angle of a triangle using the cosine rule?
A-Level Maths Edexcel C2 January 2008 Q6a ExamSolutions
This question is on the cosine rule A-Level Maths Edexcel C2 January 2007 Q9(a) : ExamSolutions
Worked solution to the above Core 2 question on finding an angle in radians using the cosine rule.

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