Sine Law

Sine Law

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.


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: \(\dfrac{a}{\sin(\textrm{A})} = \dfrac{b}{\sin(\textrm{B})} = \dfrac{c}{\sin(\textrm{C})} = 2r\).


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.

Try Buzzmath activities for free

and see how the platform can help you.