The angle at the vertex of a conical body is 120°. What is the ratio of the radius of the conical body to its slant height?

The vertex angle of the cone is 120°, so the semi-vertical angle is 60°. In the right triangle formed by axis, radius, and slant height, sin(60°) = radius/slant height = √3/2. Hence the ratio of radius to slant height is √3 : 2.