Haines was a engineer at the Snowcap base in December 1986. When the Cybermen told them to dismantle the Z-bomb, Haines, along with Ben Jackson, John Dyson and Barclay were forced to dismantle it. When the First Doctor revealed over the loudspeaker that the Cybermen planned to explode the Z-bomb in the silo, they refused to work.
When Ben released that radiation killed Cybermen, they planned to use isotopes to attack the Cybermen.
Ben set Haines and Dyson up at the end of the corridor. When the Cybermen used gas to draw Ben and Barclay out of the silo, Haines and Dyson attacked the Cybermen with the radiation, but one of the Cybermen managed to use its weapon to kill Haines. (TV: The Tenth Planet)