Last updated on June 25th, 2025
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about the Pythagorean Triples Calculator.
A Pythagorean Triples Calculator is a tool to find sets of three positive integers a, b, and c that satisfy the equation
a² + b² = c². These sets are known as Pythagorean triples.
The calculator helps quickly identify or verify such sets, saving time and effort in mathematical computations.
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the values for a and b: Input the two smaller integers into the given fields.
Step 2: Click on calculate: Click the calculate button to find the third integer, c, that completes the Pythagorean triple.
Step 3: View the result: The calculator will display the result instantly.
To calculate Pythagorean triples, one can use the formula a² + b² = c².
For example, if a and b are known, you can find c by calculating the square root of a² + b². Conversely, if c is known, one can verify if a and b form a Pythagorean triple by checking whether a² + b² equals c².
When using a Pythagorean Triples Calculator, there are a few tips and tricks to make it easier and avoid errors:
We may think that when using a calculator, mistakes will not happen. But it is possible for children to make mistakes when using a calculator.
What is the third integer in a Pythagorean triple if a = 5 and b = 12?
Use the formula: c = √(a² + b²)
c = √(5² + 12²) = √(25 + 144) = √169
c = 13
Therefore, the Pythagorean triple is (5, 12, 13).
By using the formula, the third integer c is calculated as the square root of the sum of the squares of a and b, resulting in 13.
A right triangle has legs of lengths 7 and 24. What is the length of the hypotenuse?
Use the formula: c = √(a² + b²)
c = √(7² + 24²) = √(49 + 576) = √625
c = 25
Therefore, the Pythagorean triple is (7, 24, 25).
The calculation confirms that the hypotenuse is 25, forming a Pythagorean triple with the given legs.
Can the integers 8, 15, and 17 form a Pythagorean triple?
Check using the formula: a² + b² = c²
8² + 15² = 64 + 225 = 289
17² = 289
Since both sides are equal, (8, 15, 17) is a Pythagorean triple.
The integers satisfy the equation for Pythagorean triples, confirming they form such a set.
If one leg of a right triangle is 9 and the hypotenuse is 15, what is the length of the other leg?
Use the formula: b = √(c² - a²)
b = √(15² - 9²) = √(225 - 81) = √144 b = 12
Therefore, the Pythagorean triple is (9, 12, 15).
By rearranging the Pythagorean theorem to solve for the missing leg, the result is verified as 12.
A triangle has sides 6, 8, and 10. Is this a right triangle?
Check using the formula: a² + b² = c²
6² + 8² = 36 + 64 = 100
10² = 100
Since both sides are equal, (6, 8, 10) is a Pythagorean triple, indicating it is a right triangle.
The triangle satisfies the condition for Pythagorean triples, confirming it is a right triangle.
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
: She has songs for each table which helps her to remember the tables