To complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider use a fire arrow to swing the platform towards you.
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Shoot the flammable gas to swing the platform towards you to complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider
Jump onto the platform and ride it to the next area. Keep following the path and jump down to a lower area on the left. Go up to the totem pole and release the gas. Shoot the flammable gas to release the platform.

Shoot the flammable gas to release the platform to complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider
Go back to the upper area and shoot the flammable gas with another fire arrow.

Shoot the flammable gas to swing the platform towards you to complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider
When the platform swings up jump over to it and then to the path ahead. Keep following the path and use the platform to get to the cliffs ahead. Go up and around and release the platform.

Cut the platform loose to complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider
Jump over to the released platform and jump off the other side and use the grappling hook to swing to the cliffs ahead. Release the gas. Go back over to the first platform and shoot the flammable gas.

Shoot the flammable gas to raise the platform to complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider
Ride the platform up and jump over and climb up to the path to the right. Follow the path. Shoot the flammable gas and then jump to and climb the cliff ahead.

Shoot the flammable gas to clear a path to complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider
Cut the platform loose. Keep following the path and release the gas. Jump across the nearby platform to the far platform. Use a fire arrow to raise the platform.

Shoot the flammable gas to complete the tree of life tomb in Mission of San Juan in Shadow of the Tomb Raider
Climb back around to the top area and retrace your steps a little and turn right. Go across the wooden beams to complete the tree of life tomb.