You're lost. You walk 3 km north, then 4 km east. How far are you from your start? Pythagoras to the rescue.
Drag the corners
isosceles · acute
Why north-then-east makes a right angle
North and east are perpendicular directions, so your two walked legs form the two short sides of a right triangle. The straight-line distance home is the hypotenuse — and Pythagoras hands it to you without you ever walking it.
Your turn
You walk 6 km north, then 8 km east. How far are you from your start, in a straight line?
Any walk made of straight legs at right angles can be folded into one right triangle: total all your north/south, total all your east/west, then take the hypotenuse.
Distance
Triangle 3-4-5 is the most famous right triangle. The Egyptians used a knotted rope of 12 segments to make perfect 90° angles for the pyramids.