Enigma 1329: Height of ignorance
26 April 2014
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From New Scientist #2488, 26th February 2005
A friend asked Joe, a keen rugby player, how high rugby goal posts were. Joe had no idea. So he went to the local club with two gadgets he’d made, one to measure the angle from ground level up to the top of a goal post and the other, a large pair of dividers, to measure distance.
He set the dividers to a standard distance. Then he walked 10 standard distances in a straight line from one goalpost and measured the angle to the top of the post. As a check, he walked on the same distance in the same direction and measured the angle again. Just to be certain his calculation would be correct, he walked on the same distance in the same direction and measured the angle for a third time. In calculating the height of the post Joe was surprised to find that the sum of the three angles equalled one right angle.
What was the height of the goalpost in standard distances?