How long have people been using geometry to solve real world problems?
If recent findings are any indication, it's at least 3,700 years. The application? To support the definition of a piece of property in ancient Babylon. Let's go straight to the four minute video to get the story:
We covered the story of the Plimpton 322 (P-322) clay tablet back in 2017, where it was hypothesized to be a kind of trigonometry table but the jury was out because there wasn't sufficient evidence to indicate that it was used for that purpose. The Si.427 clay tablet, which dates to the same approximate period, provides evidence that these calculations were being applied in the real world to define property boundaries. In that light, the P-322 clay tablet was an essential tool for establishing property rights in Babylon.
Reference
Daniel F. Mansfield, Plimpton 322: A Study of Rectangles, Foundations of Science (2021). DOI: 10.1007/s10699-021-09806-0.