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Sine rule
The general sine rule is
Explanation
For the angles of any ∆ ABC applies
The parts of a circle around this triangle consist of
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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.