Sine law

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any shaped triangle to the sines of its angles.





 According to the law:
 

  where a, b, and c are the lengths of the sides of a triangle, and are the opposite angles (see the figure to the right), and D is the diameter of the triangle's circumcircle.

We ca prove the sinus law by taking the height BO = h from point B to AC side:

In ABO and BCO triangles:
 

Comparing h:


In the same way, taking height to another side of triangle ABC we can prove: