Cross to the far left corner of the room. Now that you've lowered the hinged ledge here, you can use the angled metal blocks for a boost to the shelf above. Here's how:
Stand facing the lower angled block in the corner and step back until Lara bumps into the block behind her. Then jump forward onto the first slope.
Continue holding the Jump and Action buttons and Lara will backflip onto the higher higher block. . .
. . . spring forward. . .
. . . and grab the high ledge ahead.
Then you can pull up, turn around, and take a running jump over the gap where the hinged ledge was.
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