Pythagorean Theorem Calculator
Find any side of a **right triangle** using the formula: **a² + b² = c²**
Applications
* **Construction:** Ensuring corners are square, calculating diagonal distances
* **Navigation:** Finding shortest distance between two points
* **Engineering:** Calculating forces, distances, and angles in structures
* **Computer Graphics:** Distance calculations, collision detection
* **Surveying:** Measuring distances and heights
Pythagorean Triples
A **Pythagorean triple** is a set of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples:
* (3, 4, 5) - the most famous triple
* (5, 12, 13)
* (8, 15, 17)
* (7, 24, 25)
* (20, 21, 29)
Frequently Asked Questions
Q:What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of squares of the other two sides: a² + b² = c². For example, if a = 3 and b = 4, then c = √(3² + 4²) = √(9 + 16) = √25 = 5. This theorem only applies to right triangles (triangles with one 90° angle).
Q:How do I find the hypotenuse?
If you know both legs (a and b), the hypotenuse c = √(a² + b²). For example, with legs 3 and 4, c = √(9 + 16) = √25 = 5. The hypotenuse is always the longest side of a right triangle.
Q:How do I find a missing leg?
If you know the hypotenuse (c) and one leg (a), the other leg b = √(c² - a²). Similarly, if you know c and b, then a = √(c² - b²). The hypotenuse must always be greater than either leg.
Q:Does this work for all triangles?
No, the Pythagorean theorem only applies to right triangles (triangles with exactly one 90° angle). For other triangles, use the Law of Cosines or Law of Sines.