View source for Sine theorem

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For any triangle in the Euclidean plane with sides $a,b,c$ and opposite angles $A,B,C$, respectively, the equalities

$$\frac{a}{\sin A}=frac{b}{\sin B}=frac{c}{\sin C}=2R$$

hold, where $R$ is the radius of the circumscribed circle.



====Comments====
In spherical geometry the sine theorem reads

$$\frac{\sin a}{\sin A}=frac{\sin b}{\sin B}=frac{\sin c}{\sin C},$$

and in Lobachevskii geometry:

$$\frac{\sinh a}{\sin A}=frac{\sinh b}{\sin B}=frac{\sinh c}{\sin C}.$$

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  H.S.M. Coxeter,   S.L. Greitzer,   "Geometry revisited" , Math. Assoc. Amer.  (1975)</TD></TR></table>