Pythagorean Theorem Calculator
Calculate the hypotenuse or missing leg of a right triangle using the Pythagorean theorem. Free online with step-by-step results.
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5
c = √(3² + 4²) = √25.00
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Understanding the Pythagorean Theorem
The Pythagorean theorem is one of the most fundamental results in mathematics. Discovered by the ancient Greek mathematician Pythagoras, it describes the relationship between the three sides of a right triangle. If you know the lengths of any two sides, you can always find the third. This theorem is essential in geometry, trigonometry, physics, engineering, and architecture.
The Formula
a² + b² = c²
- a and b are the two legs (the sides that form the right angle).
- c is the hypotenuse (the longest side, opposite the right angle).
- To find the hypotenuse:
c = √(a² + b²) - To find a missing leg:
a = √(c² - b²)
Frequently Asked Questions
The Pythagorean theorem states that in a right 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. The formula is a² + b² = c².