The sine rule states a/sinA = $\frac{b}{sinB}$ = $\frac{c}{sinC}$ = 2R, where R is the circumradius. This provides two key capabilities: (1) relating any side to its opposite angle (use a/sinA = $\frac{b}{sinB}$), and (2) computing the circumradius (R = $\frac{a}{2sinA}$). Apply the sine rule when given: two angles and one side $\frac{AAS}{ASA}$, or two sides and a non-included angle (ambiguous case SSA). In the ambiguous case, there may be zero, one, or two triangles satisfying the given data. The sine rule also expresses sides in terms of angles: a = 2R sinA, which is useful for proving identities where you want to replace side variables with angle expressions.