How does joker die?

It's quite complex really: He was fighting batman at the top of a tower and batman was hanging of the edge. Then a joker helicopter came with a rope ladder. The joker got on the rope ladder as batman threw a bat thing with a rope at him. One end tied to the tower one to the Jokers leg. Then the helicopter flew up and Joker let go and so did the rope. Then he fell to his death.