Sine theorem

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

hold, where is the radius of the circumscribed circle.


In spherical geometry the sine theorem reads

and in Lobachevskii geometry:


[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:
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