Pythagorean Theorem
Solve for any side of a right triangle using the Pythagorean theorem.
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FAQs
How do I find a leg of the triangle if I know the hypotenuse?
Rearrange the formula: a = √(c² - b²). For example, if the hypotenuse is 10 and one leg is 6: missing leg = √(10² - 6²) = √(100 - 36) = √64 = 8.
What are Pythagorean triples?
Pythagorean triples are sets of three integers that satisfy the Pythagorean theorem exactly. Common examples: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25). Multiples of these also work: (6, 8, 10), (9, 12, 15). They are useful in construction because they guarantee a perfect right angle.
Does the Pythagorean theorem work in 3D?
Yes — the 3D extension is: d = √(x² + y² + z²) where d is the diagonal distance between two points in three-dimensional space. This formula is used in computer graphics, 3D modelling, and physics to calculate distances between points in space.