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Sine rule

The general sine rule is



For the angles of any ∆ ABC applies

The parts of a circle around this triangle consist of

The side c is the chord AB. From the center M we draw the rays MA and MB, and the line MD perpendicular to AB. Angle AMB is 2γ and therefore angle AMD is equal to γ. In the right triangle MAD we see

what you can change in

The chord AB = AD + DB = c = 2R sin γ and so we can write

Because this applies to each side of ∆ ABC, the general rule is

This is an elegant version of the sine rule.


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