Walk around to the end of the ledge, where it juts out toward the rope.
Walk to the edge and use the Walk and direction buttons to position Lara so she's squarely facing the rope.
Hop back once...
...then take a running jump and hold Action to grab the rope.
Continue to hold Action to hang onto the rope. You'll get the longest arc if you climb all the way down before starting to swing. So wait until Lara stops swinging and press Back/Down to shimmy down the rope to the bottom.
Now press the Sprint/Dash button to swing forward...
...then Jump to let go of the rope and land on the ledge. (You could also just release Action to let go, but pressing Jump adds a little extra oomph, which you'll need at times.)
Copyright © 1999- - Stellalune ( ). All rights reserved. The screenshots and videos included here were made using Bandicam and the classic Tomb Raider widescreen patch by Mr. Fourblack. Feel free to copy or print this walkthrough for personal use. By all means, share it with friends, but please include this credit line so people can send me their feedback. No part of this walkthrough may be reproduced on another site without permission.