When to Use the Cosine Rule and When to Use the Sine Rule

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The Cosine Rule and the Sine Rule are both used to find sides and angles in triangles that are not right angled. For the triangle below,

the Cosine Rule states

The Sine Rule states

Which rule to use depends on the combination of angles and sides you are given.

Given three sides, use the Cosine Rule
Given two sides and the angle between them, use the Cosine Rule
Given any two angles, use the Sine Rule
Given two sides and an angle, if the given angle is not between the two sides, use the Sine Rule 
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