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The Chinese General and the River


An old Chinese general led his army to a river with a steep bank.  Standing atop the bank, he held a stick 6 feet long perpendicular to himself.  When the near end was 0.5 feet below his eye, he sighted the opposite side of the river over the far end of the stick.  Without moving anything but his eye, he spied the near side of the river in line with a mark on the stick 2.6 feet from the near end.  Having finished gazing, he lowered a rope down the bank and found the length to be 30 feet.  What was the width of the river if his eye was 5 feet above the ground? (Qin Jiushao, Shushu jiuzhang, China, 1247)

"The Chinese General and the River," Convergence (February 2006)