The side of the triangle is 18 cm, and the radius of the circumscribed circle is 6√3 cm.

The side of the triangle is 18 cm, and the radius of the circumscribed circle is 6√3 cm. Find the angle opposite to this side. How many solutions does the problem have?

AB – side of the triangle; AB = 18 cm; R is the radius of the circumscribed circle; R = 6 √3 cm

<ACB – angle opposite to the AB side;

The formula for calculating the side of a triangle through the radius of the circumscribed circle:

AB = R * 2 sin <ACB; from here:

sin <ACB = AB: (2 * R) = 18: (2 * 6 √3) = 3 / (2 √3) = √3 / 2;

one). arcsin √3 / 2 = 60 °; 2). arcsin √3 / 2 = 120 °;

The problem has two solutions: <ACB = 60 °; <ACB = 120 °.