To jump from the dome and grab ledge below the swinging crate without getting clobbered, start by positioning Lara on the flat part of the dome farthest to the left when facing the crate. This spot is marked with an X in the screenshot above.
Walk to the edge and sidestep as far to the left as possible. Then use the Look button to check Lara's angle. Adjust her so she's facing just to the left of the center line between the two blocks that make up the ledge.
Take one hop back to set up the jump.
Then take a running jump. . .
. . . and grab the ledge. Lara should end up hanging below and to the left of the crate. Traverse to the left and pull up onto the ledge.
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