What is the Pythagorean Theorem?
Understanding one of the most famous formulas in mathematics.
The Pythagorean theorem is a fundamental rule in geometry that describes the relationship between the three sides of a right-angled triangle. It is a key part of math that has been studied for thousands of years and is used in science, engineering, and everyday life.
a² + b² = c²
The Formula Explained
The theorem states that for a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
- a and b are the lengths of the two shorter sides of the triangle.
- c is the length of the hypotenuse, which is always the longest side.
This simple formula allows you to find a missing side if you know the lengths of the other two. For instance, if you know `a` and `b`, you can find `c` by calculating `√(a² + b²)`.
Need to solve a triangle problem quickly? Try our Pythagorean Theorem Calculator.
A Simple Example
Imagine a right triangle with one side of 3 units and another of 4 units. To find the length of the longest side (the hypotenuse):
- Square the lengths of the sides: 3² = 9 and 4² = 16.
- Add the results: 9 + 16 = 25.
- Find the square root of the sum: √25 = 5.
The length of the hypotenuse is 5 units. This is a classic "3-4-5 triangle."
Real-World Applications
The Pythagorean theorem is not just for math class. It is used in many real-world situations:
- Construction: Making sure the corners of buildings are perfectly square.
- Navigation: Calculating the shortest distance between two points on a map.
- Design: Finding the diagonal size of a TV screen or computer monitor.