How to Use the Pythagorean Theorem to Find a Missing Side (With Examples)
Find the hypotenuse or a leg of a right triangle using a² + b² = c², with area, perimeter and angles shown by the calculator.
In a right triangle the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. This simple fact is used in building, navigation and everyday measuring.
Quick answer
a² + b² = c². Find c with c = √(a² + b²). Find a leg with a = √(c² − b²).
Examples
Find the hypotenuse. Legs 3 and 4: c = √(9 + 16) = √25 = 5.
Find a leg. Hypotenuse 13 and leg 5: a = √(169 − 25) = √144 = 12.
Practical: a ladder 5 m long with its foot 1.5 m from the wall reaches √(25 − 2.25) = 4.77 m up the wall.
What the calculator adds
Besides the missing side, it gives the area (½ × a × b), the perimeter and the two acute angles.
Steps
- Choose what to find: hypotenuse or a leg.
- Enter the two known sides.
- Read the result and extras.
Common Pythagorean triples
3-4-5, 5-12-13, 8-15-17, 7-24-25 and their multiples (6-8-10, 9-12-15).
Everyday uses
- Checking square corners: a 3-4-5 measurement on a floor shows a true right angle.
- Screen sizes: the diagonal of a 16 × 9 inch screen is √(256 + 81) = 18.4 inches.
- Distance on a map or grid.
Tips
- The hypotenuse is always the longest side, opposite the right angle.
- Use the same unit for all sides.
