Ms. Dunk finds a path that lea

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Ms. Dunk finds a path that leads from the entrance to the cave into the cave at a constant upward slope.  Walking from the cave's entrance up the path, she finds that it takes her exactly 8 minutes before she hits her head on the ceiling of the cave.  Crawling on her hands and knees with her meter stick, she finds that the remaining portion of the path, until it hits the ceiling of the cave, measures 10 meters.  She knows that she is five feet three inches tall, and that her average walking pace is 3 miles per hour.  To the nearest meter, how high is the cave at the entrance?

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