The situation is that the character was in the mountains and fell into an underground cave. He lands on ice and escapes with getting the wind knocked out of him and a broken arm.
Google says that you can survive a fall from about any height, depending on your rate of descent, how you land, and what you do after you bounce.
The character in question also has a bit of supernatural power which would likely cushion some of the fall.
Is twenty feet too high or believable?