Pythagorean Theorem Calculator
Calculate the hypotenuse or one of the legs of a right-angled triangle.
How to Use
- Select what you want to solve for (Hypotenuse, Leg a, or Leg b).
- Enter the lengths of the two known sides.
- Click 'Calculate' to find the length of the unknown side.
About Pythagorean Theorem
In mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
Formula
The theorem states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides: a² + b² = c².
Finding a Leg
To find the length of one of the shorter sides (legs), use the formula rearranging: a = √(c² - b²) or b = √(c² - a²).
Properties
- Applies only to right-angled triangles.
- The hypotenuse is always the longest side.
- Pythagorean triples are integer sets that perfectly fit the equation (e.g., 3, 4, 5).
Applications
- Construction and architecture to ensure square corners.
- Navigation to find the shortest distance between two points.
- Surveying and cartography.