Pythagoras Theorem

The theorem

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides:

where $c$ is the hypotenuse and $a$, $b$ are the two shorter sides.

Worked example

A rectangular sports field is 48 meters wide and 55 meters long. A coach jogs from one corner along the width, then along the length to the opposite corner, and finally cuts straight back across the field to where they started. How far does the coach jog in total?

Solution: The first two legs of the jog are the two sides of the rectangle, 48 m and 55 m. The final leg, straight back to the start, is the diagonal of the rectangle, the hypotenuse of a right triangle with legs 48 and 55:

Total distance jogged: $48 + 55 + 73 = 176$ meters.