math

In order to estimate the height 'h' of a tall pine tree, a student places a mirror on the ground and stands where she can see the top of the tree. The student is 6 feet tall and stands 3 feet from the mirror which is 11 feet from the base of the tree. Another student also wants to see the top of the tree. The other student is 5.5 feet tall. If the mirror is to remain 3 feet from the student's feet, how far from the base of the tree should the mirror be placed?

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  1. The only tricky part in this question is to ignore data which is irrelevant, like the 6 ft girl's initial mirror placement.

    The only fact we care about is that we have two similar right-angled triangles, formed by the second student and the mirror, and the tree and the mirror.
    Make that sketch.
    let the distance of the mirror for the tree for the second experiment be x
    then x/11 = 3/5.5
    x = 33/5.5 = 6 ft

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