In trigonometry, the law of sines (also known as the sine law, sine formula, or sine rule) is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. According to the law,
where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right). These fractions are equal to the diameter of the triangle's circumcircle. Sometimes the law is stated using the reciprocal in this equation:
The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the formula gives two possible values for the enclosed angle, leading to an ambiguous case.
The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in a general triangle, with the other being the law of cosines.
Read more about Law Of Sines: Examples, Numeric Problems, Some Applications, The Ambiguous Case, Relation To The Circumcircle, Spherical Case, Hyperbolic Case, Unified Formulation, History, Derivation, A Law of Sines For Tetrahedra
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