Runners in a long distance race start out going 5 kilometers south and then head west for the remainder of the race. The finish line is 13 kilometers from the starting line. How far did the runners travel?
You may recognize the numbers as belonging to the (5, 12, 13) Pythagorean triple. The runners traveled 12 km west after traveling 5 km south. Their total distance was ... 5 km +12 km = 17 km
_____ By the Pythagorean theorem, ... (straight-line distance)² = (distance south)² +(distance west)² In km, this is 13² = 5² +(distance west)² 169 -25 = (distance west)² √144 = 12 = distance west
