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The sine rule

The sine rule holds in every triangle, not just right triangles. The ratio between a side and the sine of the opposite angle is the same for all three sides. It is used when you know two angles and a side, or two sides and an angle that is not between them.

asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}the sine rule

Symbols

a, b, ca,\ b,\ csides
A, B, CA,\ B,\ Cangles opposite the sides°

Example

A=40∘A = 40^\circ, B=60∘B = 60^\circ and a=8a = 8: b=8sin⁡60∘sin⁡40∘≈10.78b = \frac{8\sin 60^\circ}{\sin 40^\circ} \approx 10.78.

With two sides and an angle not between them, there can be two triangles.
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Part of Mathematics 1T: Trigonometry.