The sine rule is one of a pair of rules useful in solving triangles. It concerns the ratio between the length of a side and its opposite angle.

Given a triangle with vertices A,B,C and edges a,b,c opposite their respective angles, the sine rule states:

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

It is possible, using this method, to solve a triangle when given a side length and any two angles. It is also possible to solve the case given two sides and one non-included angle - although an ambiguous result will be given, which must be checked against the rule:

A+B+C = 180°.

For an included angle, or three side lengths, use the cosine rule.

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