In a triangle ABC AB = 4√3, BC = 3. The area of a triangle is 3√3. Find the radius of the circle circumscribed

In a triangle ABC AB = 4√3, BC = 3. The area of a triangle is 3√3. Find the radius of the circle circumscribed about the triangle if the center lies inside the triangle.

We use the shape of the area of the triangle through the sides and the angle between them.

Savs = AB * BC * SinABC / 2.

3 * √3 = 4 * √3 * 3 * SinABC / 2.

SinABC = 2 * 3 * √3 / 4 * √3 * 3 = 1/2.

Angle ABC = 30.

By the cosine theorem, we determine the length of the side AC of the triangle ABC.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos30 = 48 + 9 – 2 * 4 * √3 * 3 * √3 / 2 = 57 – 36 = 21.

AC = √21 cm.

R = AC / 2 * Sin30 = √21 / (2 * 1/2) = √21 cm.

Answer: The radius of the circle is √21 cm.