Trigonify

Topics · 2 identities

Law of Sines

Relating each side of any triangle to the sine of its opposite angle.

Law of Sines: a/sin A = b/sin B = c/sin C

asin⁡A=bsin⁡B=csin⁡C\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

In any triangle, each side divided by the sine of its opposite angle gives the same value: a/sin A = b/sin B = c/sin C. Use it for AAS, ASA, and SSA. SSA is the ambiguous case - it can yield two triangles, one, or none, so always check whether a second angle also fits.

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Law of Sines circumradius form: a/sin A = 2R

asin⁡A=2R\dfrac{a}{\sin A} = 2R

The common ratio in the Law of Sines is not arbitrary: it equals 2R, twice the radius of the triangle's circumscribed circle. That turns the Law of Sines into a way of finding the circumradius from any one side and its opposite angle.

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