During his escape from the police, Rambo is eventually located and chased.
He then gets stuck on the top of a very high cliff, but decides to jump using the tops of the trees to lessen his fall.
The famous jump scene really happened during the Vietnam War, and it happened to a MacVsog team, according to one of author John Plaster's books.
A SOG team, located in hostile territory and chased by a full Vietcong battalion (eight soldiers followed by something like one hundred enemies) found themselves stuck on the top of a high cliff.
When faced with the possibility of being captured or killed, the soldiers jumped from the cliff, hoping to use the triple canopy jungle to lessen the fall.
Once on the ground and under the very thick jungle, they were also out of the line of sight of their chasers, who couldn't do anything more than blindly shoot in their direction.
No Vietcong dared to jump to continue chasing them.
All of the soldiers injured themselves in the fall, but they all returned to their base alive.