Pythagorean Theorem Calculator
Solve for any side of a right triangle using the Pythagorean theorem.
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Solve Right Triangles with the Pythagorean Theorem
Our Pythagorean Theorem Calculator helps you find the length of any missing side of a right-angled triangle, along with its angles, area, and perimeter.
What is the Pythagorean Theorem?
The Pythagorean theorem is a cornerstone of Euclidean geometry, describing the relationship between the three sides of a right-angled triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This is famously expressed as the equation a² + b² = c².
How It Works: The Formula
The calculator rearranges the core formula to solve for the unknown side:
Solve for Hypotenuse (c): c = √(a² + b²)
Solve for Side (a or b): a = √(c² - b²)
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental principle in geometry that states that in a right-angled triangle, the square of the length 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.
How do you use the Pythagorean theorem?
You can use the Pythagorean theorem to find the length of a missing side of a right-angled triangle when you know the lengths of the other two sides. If you know sides 'a' and 'b', you can find the hypotenuse 'c' with c = √(a² + b²). If you know 'a' and 'c', you can find 'b' with b = √(c² - a²).
What is a Pythagorean triple?
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy the Pythagorean theorem, a² + b² = c². The most famous example is (3, 4, 5). Other common triples include (5, 12, 13) and (8, 15, 17).
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