In a triangle, the name given to the relationship of proportionality between the measures of the sides and the sine values of the angles opposite each of these sides.

### Property

Consider the radius \(r\) of any circumscribed circle of a triangle with sides \(a\), \(b\) and \(c\) and angles *A*, *B* and *C*; this gives us the following relationship: \(\dfrac{a}{\sin(\textrm{A})} = \dfrac{b}{\sin(\textrm{B})} = \dfrac{c}{\sin(\textrm{C})} = 2r\).

### Example

Consider triangle *ABC* in which side *AB* measures 15 cm and angles *ABC* and *BAC* measure 60° and 50° respectively. We can deduce that angle *BCA* measures 70°, since 180° − (60° + 50°), then we can calculate the measure *a* of side *BC* by posing \(\dfrac{a}{\sin(50)} = \dfrac{15}{\sin(70)}\).

Which gives *a* ≈ 12.23 cm.