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Two vertical poles 2 meters and 8 meters high stand apart on a horizontal plane. What is the height in meters of the point of intersection of the lines joining the top of each pole to the bottom of the other pole?
Two vertical poles 2 meters and 8 meters high stand apart on a horizontal plane. What is the height in meters of the point of intersection of the lines joining the top of each pole to the bottom of the other pole?
The height of the point of intersection can be found using similar triangles. The two poles and the point of intersection form two similar right triangles. The height of the point of intersection is therefore (8/6) times the distance between the bases of the poles, which is sqrt(6^2 - 2^2 - 8^2) = sqrt(20). Therefore, the height of the point of intersection is approximately 9.8 meters.