A boy of mass m_boy stands at the edge of a merry-go-round of radius R = 3.5 m and mass m_mgr, and both are initially at rest. The boy then walks along the edge of the merry-go-round. After walking a distance of 21 m relative to the merry-go-round, the boy finds that the merry-go-round has rotated through an angle of 20°. Find the ratio of m_boy to m_mgr.