Side AB of triangle ABC is 7. The opposite angle C is 30 degrees. Find the radius of the circle described around this triangle.

From the extended sine theorem:
a / sinA = 2R,
where a is the side of the triangle, A is the angle opposite to the side a, R is the radius of the circle circumscribed about the triangle.
Substitute the known values and find the length of the radius of the circle circumscribed about the triangle ABC:
7 / sin30 = 2R;
7: 1/2 = 2R;
7 * 2 = 2R;
2R = 14;
R = 14/2;
R = 7.
Answer: R = 7.