Pythagorean Theorem Calculator

For a right triangle, find the longest side (hypotenuse) from the two shorter sides.

How the Math Works

The Pythagorean Theorem is a fundamental principle in geometry that relates the sides of a right-angled triangle. When given the lengths of the two legs (a and b), the theorem allows you to calculate the length of the hypotenuse (c) using the formula c = sqrt(a^2 + b^2). This works because squaring each leg's length and adding them together gives the square of the hypotenuse's length, which is then square-rooted to find its actual value. The relationship holds true for all right triangles, making it an essential tool for solving problems involving right angles.

Practical Applications

This calculation is widely used in construction, architecture, and engineering to ensure structures are built with precise right angles. For example, when constructing a roof, laying out a foundation, or designing furniture, knowing two sides of a right triangle allows you to determine the third side for accurate measurements. It's also applied in navigation and surveying to calculate distances between points on a flat surface, and in computer graphics for determining pixel distances or object sizes in 2D space.

Day-to-Day Use

In everyday life, this theorem helps with practical tasks like determining the correct size for a TV or monitor to fit a specific wall space, or calculating the shortest path between two points when walking or driving. DIY enthusiasts use it to build projects like garden beds or decks with accurate corner angles, and students often apply it when solving real-world geometry problems, such as measuring the diagonal of a room or checking if a piece of furniture will fit through a doorway.

Worked example

Legs 3 and 4 -> c = sqrt(9 + 16) = sqrt(25) = 5.

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