Law of Sines

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

asinA=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.

obliquecircumradius

Related Law of Sines identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Law of Sines questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.