Two vertical poles 20 m and 80 m tall stand on level ground. The lines joining the top of each pole to the foot of the other cross at X. How high is X above the ground?

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Accepted Answer

16 m. If the poles are D apart and X is x from the shorter pole, similar triangles give h/20 = (D − x)/D and h/80 = x/D. Adding, h(1/20 + 1/80) = 1, so h = 20 × 80/100 = 16 m — whatever the distance D.

Two vertical poles 20 m and 80 m tall stand on level ground. The lines joining the top of each pole to the foot of the other cross at X. How high is X above the ground?

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