Mieko, who is 1.53 m tall, wishes to find the height of a tree. She walks 21.66 m from the base of the tree along the shadow of the tree until her head is in a position where the tip of her shadow exactly overlaps the end of the tree top's shadow. She is now 6.42 m from the end of the shadows. How tall is the tree? Round to the nearest hundredth.
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