Evidence for the statement that Rigel II is less than ninety light years from Earth is specifically that, in "Two Days and Two Nights", the NX-classEnterprise sets a milestone several months after undertaking a mission to Rigel X (which it visits in ENT pilot episode "Broken Bow") by becoming the first Earth ship to travel ninety light years away from the Sol system.
According to Star Trek: Star Charts (pp. 52, 59, "United Federation of Planets I"), Rigel II, also known as Beta Rigel II, was an M-class planet. The planet was a member planet of both the United Rigel Colonies and the United Federation of Planets. Rigel IV was admitted, along with the United Rigel Colonies, to the Federation in 2202.