The distance formula is used to find the distance between two points in a cartesian plane or in space. Apart from its use in various proofs and conjectures, this formula leads to methods to solve real life problems, for example finding the true direction of a jet plane, for calculating length of a lake, height of a building, length of a bridge, length of a ladder to reach a particular window during emergency evacuations, finding the shortest distance through a field, or through waters to reach a particular spot, etc.
Athletes (soccer players) use this formula elegantly in determining the exact length of the pass that is to be thrown so that it is collected by the intended receiver neatly. Advertising personnel use it in advertising television (and other display) screens, because these units are advertised by giving the approximate length of the diagonal of its screen.
This formula is thus indispensable to many careers that include transportation engineering, aeronautics, sports engineering, architects, oceanographers, rescue and emergency services, advertisers, etc.