High School Pythagorean Theorem Calculator
Solve for any side of a right triangle using a² + b² = c².
Resulting Length
Step-by-Step
Triangle Visualization
Using the Pythagorean Theorem Calculator
The Pythagorean Theorem is a fundamental principle in geometry that describes the relationship between the three sides of a right-angled triangle. It states that 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 written as:
Here, c represents the length of the hypotenuse, while a and b represent the lengths of the triangle’s legs. This theorem allows us to calculate the length of any side if the other two are known.
Why use a Pythagorean Theorem Calculator?
While manual calculation is straightforward for “Pythagorean Triples” like 3-4-5 or 5-12-13, real-world problems often involve square roots of non-perfect squares. For example, if legs are 5 and 7, the hypotenuse is √74, which is approximately 8.602. This tool instantly performs the squaring, adding (or subtracting), and square-rooting operations, providing both exact and decimal approximations.
Applications
This theorem isn’t just for geometry class. Builders use it to ensure corners are square (the 3-4-5 method). GPS systems use a variation of it to calculate distances between coordinates. It is also essential in physics for resolving vectors into components.
FAQ
Yes, this tool is completely free for all students and teachers to use.
No. This theorem strictly applies only to right-angled triangles (triangles with one 90-degree angle).
Yes. By rearranging the formula to a² = c² – b², the tool can solve for a missing leg if you know the hypotenuse.
It is a set of three positive integers that fit the theorem perfectly, such as (3, 4, 5) or (6, 8, 10).