Law of Sines

Let , , and  be the lengths of the legs of a triangle opposite angles , , and . Then the law of sines states that

(1)

where  is the radius of the circumcircle. Other related results include the identities

(2)

(3)

the law of cosines

(4)

and the law of tangents

(5)

The law of sines for oblique spherical triangles states that

(6)

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 79, 1972.

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 148, 1987.

Coxeter, H. S. M. and Greitzer, S. L. "The Extended Law of Sines." §1.1 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 1-3, 1967.