Pythagorean Theorem Calculator
Calculate using Pythagorean theorem
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle: a² + b² = c², where c is the hypotenuse (longest side) and a, b are the other two sides. Enter any two sides to calculate the third.
How do I find the hypotenuse of a right triangle?
Hypotenuse c = √(a² + b²). For a triangle with sides 3 and 4: c = √(9 + 16) = √25 = 5. This is the classic 3-4-5 Pythagorean triple.
What are Pythagorean triples?
Pythagorean triples are sets of three integers that satisfy a² + b² = c². Common triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Any multiple of a triple is also a triple: (6,8,10), (9,12,15).
How is the Pythagorean theorem used in real life?
Construction workers use it to ensure right angles (3-4-5 method). It calculates diagonal distances, screen sizes (diagonal of a TV), straight-line distance between two points, and ladder reach against a wall.
Does the Pythagorean theorem work in 3D?
Yes. The 3D distance formula extends it: d = √(a² + b² + c²). The space diagonal of a box with dimensions 3×4×5 is √(9+16+25) = √50 ≈ 7.07 units.