The Pythagorean theorem can find any missing side of a right triangle, as long as you know the other two.
Finding the hypotenuse (the longest side): c = √(a² + b²). Square both legs, add them, take the square root.
Finding a leg (one of the shorter sides): a = √(c² − b²). Square the hypotenuse, subtract the square of the known leg, take the square root.
The converse also works: if three sides satisfy a² + b² = c², the triangle IS a right triangle. You can use this to verify a right angle.
Remember
Finding hypotenuse → add the squares. Finding a leg → subtract the squares. Always square first, then take the root at the end.
Real World
If a ladder leans against a wall, you know the height of the wall (one leg) and the distance from the wall to the foot of the ladder (other leg) — the Pythagorean theorem tells you exactly how long the ladder needs to be.
Feeling ready?
Put this concept to work with a practice workout.