Calculatrice du Théorème de Pythagore
Trouver le côté manquant d'un triangle rectangle
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- 1a² = 3² = 9.0000
- 2b² = 4² = 16.0000
- 3a² + b² = 25.0000
- 4c = √25.0000 = 5.0000
Pythagorean Theorem
In a right triangle, the square of the hypotenuse (the side opposite the right angle) equalscalculators.pythagorean.pythagoreanDesc
Common Pythagorean Triples
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Sources et méthodologie
a² + b² = c²Pythagorean theorem for right triangles
Votre prochaine étape
How to Use the Pythagorean Theorem Calculator
The Pythagorean theorem calculator finds the missing side of a right triangle when you know two sides. Enter any two sides and instantly see the third, along with a visual diagram showing your triangle to scale.
The Pythagorean Theorem
For any right triangle with legs a and b and hypotenuse c:
a² + b² = c²
The hypotenuse (c) is always the longest side, opposite the 90° angle.
Solving for Each Side
- Finding the hypotenuse: c = √(a² + b²)
- Finding a leg: a = √(c² - b²) or b = √(c² - a²)
Pythagorean Triples
Pythagorean triples are sets of three whole numbers that satisfy the theorem. Common triples include:
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
Any multiple of a Pythagorean triple is also a triple (e.g., 6, 8, 10).
Distance Between Two Points
The Pythagorean theorem also calculates the distance between two points (x₁, y₁) and (x₂, y₂):
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Real-World Applications
- Construction: Checking if corners are square (3-4-5 rule)
- Navigation: Finding direct distances
- Screen sizes: Calculating diagonal measurements
- Ladders: Determining safe placement angles
Related Calculators
For more triangle calculations, use our square footage calculator. For slope calculations, try our slope calculator.
Questions fréquemment posées
For a right triangle with legs a and b and hypotenuse c: a² + b² = c². To find the hypotenuse, add the squares of the legs and take the square root. To find a leg, subtract the square of the known leg from the hypotenuse squared, then take the square root.
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c². Common examples: 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). These are useful for quick mental calculations.
No, the Pythagorean theorem only works for right triangles. For other triangles, use the Law of Cosines: c² = a² + b² - 2ab·cos(C). When angle C is 90°, cos(C) = 0, and this simplifies to the Pythagorean theorem.
The distance between two points (x₁, y₁) and (x₂, y₂) forms a right triangle. The horizontal distance is |x₂ - x₁| and vertical distance is |y₂ - y₁|. These are the legs, so distance d = √[(x₂ - x₁)² + (y₂ - y₁)²].
The 3-4-5 rule verifies right angles on job sites. Measure 3 feet along one edge, 4 feet along the other, and if the diagonal is exactly 5 feet, the corner is square (90°). Any multiple works: 6-8-10, 9-12-15, 12-16-20.
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