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.


In spherical geometry the sine theorem reads


and in Lobachevskii geometry:

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


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