# Sine theorem

From Encyclopedia of Mathematics

For any triangle in the Euclidean plane with sides and opposite angles , respectively, the equalities

hold, where is the radius of the circumscribed circle.

#### Comments

In spherical geometry the sine theorem reads

and in Lobachevskii geometry:

#### References

[a1] | H.S.M. Coxeter, S.L. Greitzer, "Geometry revisited" , Math. Assoc. Amer. (1975) |

**How to Cite This Entry:**

Sine theorem.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Sine_theorem&oldid=12252

This article was adapted from an original article by Yu.A. Gor'kov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article