In a triangle, the two angles are 120 degrees and 45 degrees. The side opposite the smaller of these angles is 28 in.

In a triangle, the two angles are 120 degrees and 45 degrees. The side opposite the smaller of these angles is 28 in. Find the radius of the circumscribed circle and the side of the triangle that lies opposite the 120 degree angle.

To determine the length of the side of the speaker, which lies opposite the angle 120, we apply the theorem of sines.
AC / SinABC = BC / SinBAC.
AC = BC * Sin120 / Sin45.
AC = 28 * (√3 / 2) / (√2 / 2) = 14 * √3 * 2 / √2 = 14 * √6 cm.
Determine the radius of the circle circumscribed about the triangle.
BO = R = AC / 2 * Sin120 = 14 * √6 / 2 * (√3 / 2) = 14 * √2 cm.
Answer: The radius of the circumscribed circle is 14 * √2 cm, the length of the AC side is 14 * √6 cm.