In the following identities, A, B and C are the angles of a triangle and a, b and c are the lengths of sides of the triangle opposite the respective angles.
Law of sines
The Law of Sines (also know as the "sine rule") for an arbitrary triangle states:
where R is the radius of the circumcircle of the triangle.
Law of cosines
The Law of Cosines (also known as the cosine formula, or the "cos rule") is an extension of the Pythagorean Theorem to arbitrary triangles:
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- or equivalently:
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Law of tangents
The Law of Tangents:
![LaTex: \frac{a+b}{a-b}=\frac{\tan\left[\frac{1}{2}(A+B)\right]}{\tan\left[\frac{1}{2}(A-B)\right]}](http://www.forkosh.dreamhost.com/mimetex.cgi?\frac{a+b}{a-b}=\frac{\tan\left[\frac{1}{2}(A+B)\right]}{\tan\left[\frac{1}{2}(A-B)\right]})