Right Triangle Inputs
Enter two sides to find the third.
Visualization
Properties of Right Triangles
Fundamental principles of Euclidean geometry.
The Pythagorean Theorem is one of the most famous geometric theorems, stating that for any right-angled triangle, the square of the hypotenuse ($c$) is equal to the sum of the squares of the other two sides ($a$ and $b$). This relationship is essential in architecture, engineering, and physics.
- Standard:
- Solving for Hypotenuse:
- Solving for Leg:
Pythagorean Theorem Guide Guide
How to Use
- 1Select the side you want to calculate (Hypotenuse C, Leg A, or Leg B).
- 2Enter the lengths of the two known sides.
- 3Click calculate to solve for the missing side.
- 4View the step-by-step derivation below.
Formula & Logic
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
Practical Applications
Construction & Carpentry
Ensure corners are perfectly square (90 degrees) by using the 3-4-5 rule or calculating diagonals for framing.
Distance Calculation
Calculate the shortest path (as the crow flies) between two points if you know the horizontal and vertical distances.
Screen Dimensions
Determine the diagonal screen size of a TV or monitor given its width and height.
Frequently Asked Questions
Q.What is a right-angled triangle?
A right-angled triangle is a triangle in which one angle is exactly 90 degrees.
Q.Does the theorem work for all triangles?
No, the Pythagorean Theorem only applies to right-angled triangles. For other triangles, you would need to use the Law of Cosines.
Q.What is a Pythagorean Triple?
A Pythagorean Triple is a set of three positive integers a, b, and c, such that a² + b² = c². Common examples include (3, 4, 5) and (5, 12, 13).