A ten-foot bamboo snaps, tip touching ground three feet away — how high did it break?
A bamboo stalk stands 10 feet tall. It snaps partway up, and the broken top bends over until its tip touches the ground exactly 3 feet from the base of the stalk. The unbroken lower section stays perfectly vertical, and the broken upper section stays perfectly straight as it leans. How far up the stalk did the break occur?
Reveal the answer
4.55 feet up from the ground. If the break is at height h, the fallen top section has length 10−h and forms the hypotenuse of a right triangle with legs h and 3, so h² + 3² = (10−h)², giving 20h = 91 and h = 4.55 feet. This is one of the earliest recorded uses of the Pythagorean relationship, found in the 'right triangles' chapter of The Nine Chapters on the Mathematical Art, China's foundational mathematics text, compiled anonymously over centuries into its classic form by roughly the 1st century CE.