Use a rope arrow to pull the end of the beam with the golden bucket toward you. This also drags the wooden bucket off the ledge and through the waterfall, but with the bottom of the bucket open, it won"t hold water.
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Shoot the rope-wrapped latch on the side of the wooden bucket to close the flap on the bottom.
Then shoot the upper end of the beam (above the wooden bucket) to pull the beam around toward you.
Now that the bucket is latched closed, when it moves under the waterfall it fills with water.
This causes that end of the beam to tip downward and raises the other end with the golden bucket.
Now shoot the latch again to open the bucket so the water begins to drain out.
Aim a little bit above the latch and then shoot it once more as the bucket rises. The goal is to close the bucket before all the water drains out.
When the wooden bucket is half full, it weighs about the same as the golden bucket, and the beam balances. If this doesn"t work the first time, drag the closed bucket through the waterfall to refill it and try again.
Once the beam is balanced, jump across to the platform at the center of the armature and from there to the golden bucket.
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Lara"s weight swings the golden bucket forward into the wall of ice, freeing the trebuchet.