Pythagorean Theorem Calculator

Solving Right Triangles

This calculator applies the Pythagorean theorem, a fundamental principle of geometry, to find the length of a missing side of a right-angled triangle. Enter the lengths of any two sides to solve for the third.

The Pythagorean Theorem Explained

For a right triangle with legs (the two shorter sides) a and b, and a hypotenuse (the longest side, opposite the right angle) c, the theorem states: a² + b² = c² By rearranging this formula, we can solve for any missing side:

• To find the hypotenuse (c): c = √(a² + b²)
• To find a leg (a): a = √(c² - b²)
• To find a leg (b): b = √(c² - a²)

How to Use the Calculator

1. Choose Side to Solve For: Select whether you are solving for leg 'a', leg 'b', or the hypotenuse 'c'.
2. Enter Known Sides: Input the lengths of the two sides that you know. The field for the side you are solving for will be disabled.
3. Calculate: The calculator will display the length of the missing side.

Real-World Example

You have a right triangle where one leg (a) is 3 units long and the other leg (b) is 4 units long. You want to find the length of the hypotenuse (c).

1. Select 'Hypotenuse c' to solve for.
2. Enter 3 for Side a and 4 for Side b.
3. Calculation: c = √(3² + 4²) = √(9 + 16) = √25 = 5 The calculator will show that the hypotenuse is 5 units long.

Frequently Asked Questions (FAQ)

• Can I use this for any triangle? No, the Pythagorean theorem only applies to right-angled triangles (triangles with one 90-degree angle).
• What happens if I enter a leg that is longer than the hypotenuse? The calculator will show an error, as this is geometrically impossible. The hypotenuse is always the longest side of a right triangle.
• What are Pythagorean triples? These are sets of three integers that perfectly satisfy the theorem, like (3, 4, 5) or (5, 12, 13).