In trigonometry, the law of sines (or sine law) is a statement about arbitrary triangles in the plane. If the sides of the triangle are (lowercase) a, b and c and the angles opposite those sides are (capital) A, B and C, then the law of sines states
This formula is useful to compute the remaining sides of a triangle if two angles and a side is known, a common problem in the technique of triangulation. It can also be used when two sides and one of the nonenclosed angles are known; in this case, the formula may give two possible values for the enclosed angle. When this happens, often only one result will cause all angles to be less than 180°; in other cases, there are two valid solutions to the triangle.
The reciprocal of the number described by the sine law (i.e. a/sin(A)) is equal to the diameter D of the triangle's circumcircle (the unique circle through the three points A, B and C). The law can therefore be written
Also see triangulation, cosine law, and trigonometry.
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