A circle is circumscribed about a triangle. If one of the angles of the triangle is 120°, and the radius of the circumscribed circle is r, what is the length of the side opposite the 120° angle?
\(r\sqrt{3}\)
For a triangle with circumradius \(R\), the Law of Sines (extended form) states:
\(\dfrac{a}{\sin A} = 2R\)
where \(a\) is the side opposite angle \(A\).
Apply with \(A = 120^{\circ},\ R = r\):
\(a = 2r \cdot \sin 120^{\circ}\)
Use \(\sin 120^{\circ} = \dfrac{\sqrt{3}}{2}\):
\(a = 2r \cdot \dfrac{\sqrt{3}}{2} = r\sqrt{3}\)
Hence, the answer is option A.
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