Law of sines/Elementary-geometric/Exercise

Prove by elementary geometric considerations the Sine theorem, i.e. the statement that in a triangle the equalities

${}{\frac {\sin \alpha }{a}}={\frac {\sin \beta }{b}}={\frac {\sin \gamma }{c}}\,$

hold, where ${}a,b,c$ are the side lengths of the edges and ${}\alpha ,\beta ,\gamma$ are respectively the opposite angles.

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