In triangle ABC, angle B is 56 degrees, angle C is 64 degrees, BC = 3√3. Find the radius

In triangle ABC, angle B is 56 degrees, angle C is 64 degrees, BC = 3√3. Find the radius of the circle circumscribed about this triangle.

In the triangle ABC, we determine the value of the angle BAC.

Angle BAC = (180 – ABC – AСB) = (180 – 56 – 64) = 60.

Knowing the length of one of the sides of the triangle and the value of the angle opposite to this side, we determine the radius of the circle described around the triangle.

R = ОА = ВС / 2 * SinВАС = 3 * √3 / 2 * (√3 / 2) = 3 * √3 / √3 = 3 cm.

Answer: The radius of the circumscribed circle is 3 cm.