When the cut scene finishes, go around behind the carved panel.
The slope here is too steep to climb. So climb the carved stone handholds on the left and jump back to grab the ledge behind. Pull up.
Once Lara is standing on that ledge, turn to face the top of the slope, jump off the ledge and immediately press Jump again to snag the metal grapple point above. Then either swing to the flat spot at the top of the slope and climb onto the ledge on the right, or shorten the cable and swing directly to that ledge. Note that Lara can't climb up on the left side of the ledge where it has crumbled, only on the right where it's intact.
Once Lara is standing on that ledge, turn to face the next slope.
Again, double-jump off the edge to extend the grapple. Swing and jump to the flat spot above the second slope. Continue to CHECKPOINT 16.
I'm sorry about the slightly awkward third and fourth screenshots. I couldn't get both the ledge and the grapple point in the same shot.
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