The Pythagorean Theorem
a² + b² = c²
Where c is the hypotenuse and a, b are the legs
The Pythagorean theorem is one of the most fundamental theorems in mathematics. It describes the relationship between the sides of a right triangle: the square of the hypotenuse equals the sum of squares of the other two sides.
Pythagorean Theorem Formulas
Find Hypotenuse
c = sqrt(a² + b²)
Find Leg A
a = sqrt(c² - b²)
Find Leg B
b = sqrt(c² - a²)
Common Pythagorean Triples
Pythagorean triples are sets of positive integers that satisfy a² + b² = c²:
(3, 4, 5)
3² + 4² = 5²
(5, 12, 13)
5² + 12² = 13²
(6, 8, 10)
6² + 8² = 10²
(7, 24, 25)
7² + 24² = 25²
(8, 15, 17)
8² + 15² = 17²
(9, 12, 15)
9² + 12² = 15²
(9, 40, 41)
9² + 40² = 41²
(10, 24, 26)
10² + 24² = 26²
(12, 16, 20)
12² + 16² = 20²
(12, 35, 37)
12² + 35² = 37²
Applications of the Pythagorean Theorem
Construction
Ensuring walls are perpendicular, calculating diagonal measurements, and checking if corners are square.
Navigation
Calculating direct distance between two points when traveling north/south and east/west.
Physics
Vector analysis, resolving forces into components, and calculating resultant magnitudes.
Computer Graphics
Distance calculations between pixels, collision detection, and 3D rendering.
Frequently Asked Questions
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