As darkness approached, Emek and Luna used an old expedition map to find a hidden base camp. One possible route followed two perpendicular trail sections measuring 10 kilometers and 24 kilometers. Luna used the Pythagorean Theorem to find that a direct trail between their position and camp would be 26 kilometers long. The map showed another route forming a different right triangle. Its diagonal path was 25 kilometers, and one perpendicular side was 20 kilometers. Emek calculated the unknown side as 15 kilometers because 15 squared plus 20 squared equals 25 squared. Following the two perpendicular sections of that route would therefore require 35 kilometers. They compared the choices: the 26-kilometer direct trail was 9 kilometers shorter. After checking both calculations, Emek and Luna chose the shorter path and reached the hidden base camp before nightfall.