How do you measure an island's height without ever reaching it?
A surveyor needs the height of a distant sea island and its distance from shore, but can't cross the water to measure either one directly. All that's available on land: two identical vertical poles, a horizontal sighting bar, and the ability to pace out distances precisely. How can two sightings taken entirely from dry land pin down both numbers?
Reveal the answer
Plant the two poles a measured distance apart in a straight line with the island's peak, then sight the peak over the top of each pole in turn; the shift between the two sightings lets similar triangles solve for both the island's height and its distance. Liu Hui laid out this method, plus eight similar surveying problems, in 263 CE in the Haidao Suanjing (Sea Island Mathematical Manual), the earliest surviving Chinese text on trigonometric surveying.
— Liu Hui, Haidao Suanjing (Sea Island Mathematical Manual) — 263 CE