# Pythagorean Theorem (Right Triangle) Calculator

## Solve right triangles using the Pythagorean theorem

The calculator will try to find all sides of the right-angled triangle (the legs and the hypotenuse) using the Pythagorean theorem. It will also find all angles, as well as perimeter and area. The solution steps will be shown.

The Pythagorean Theorem Calculator is a specialized geometry solver designed to help you quickly and easily find the length of a missing side of a right triangle. Using the Pythagorean Theorem, this calculator is the perfect tool for anyone looking to validate their work.

## How to Use the Pythagorean Theorem Calculator?

### Input

You should know the lengths of at least two sides of the right triangle. If you know the legs of the triangle but not the hypotenuse:

- enter the values for $$$a$$$ and $$$b$$$.
- leave the $$$c$$$ field blank.

If you know the hypotenuse $$$c$$$ and one leg (either $$$a$$$ or $$$b$$$):

- input the hypotenuse $$$c$$$ and the known leg.
- leave the other side's field blank.

### Calculation

After entering the known side lengths, click the "Calculate" button.

### Result

The Pythagorean Theorem Calculator will instantly compute and display the length of the missing side.

## What Is a Right Triangle?

A right triangle, also known as a right-angled triangle, is a triangle with one angle that is exactly 90 degrees (a right angle). The side opposite this right angle is the longest and is called the hypotenuse. The other two sides that form a right angle are called the legs of the triangle.

## What Is the Pythagorean Theorem?

The Pythagorean Theorem is a fundamental theorem in geometry that describes a relationship between the sides of a right triangle. It states that, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this relationship is expressed as

$$c^2=a^2+b^2$$In this equation:

- $$$c$$$ is the hypotenuse—the side opposite the right angle and is the longest side of the triangle.
- $$$a$$$ and $$$b$$$ are the two other sides adjacent to the right angle.

This theorem has been known and used by many ancient civilizations, including the Babylonians, Chinese, and Indians. However, it's traditionally attributed to the Greek mathematician Pythagoras, and that's where its name originates.

**Example**

Imagine a right triangle with sides $$$a=3$$$ and $$$b=4$$$ units. Find the hypotenuse length $$$c$$$:

$$c^2=3^2+4^2$$$$c^2=25$$Taking the square root of both sides, we get that $$$c=5$$$ units.

**Practical Applications**

The Pythagorean Theorem isn't just a theoretical concept. It's extensively used in various practical applications, from determining the shortest distance between two points (think of GPS technology) to architectural designs and construction. Engineers, architects, and even computer scientists find uses for this theorem in their respective fields.

## Why Choose Our Pythagorean Theorem Calculator?

### Accuracy

In mathematical calculations, accuracy is of paramount importance. Our calculator uses reliable algorithms that ensure you get correct results every time.

### User-Friendly Interface

We've built our tool with the users in mind. Its intuitive design means you don't need to be a math expert to use it. With clear input and output sections, everything is easy to understand.

### Fast Results

Our calculator provides answers almost instantly. This saves you time, especially if you are solving multiple problems.

### Versatility

Whether you are a student, teacher, engineer, or hobbyist, our calculator is built to meet a wide range of needs.

### FAQ

#### What is the Pythagorean Theorem Calculator used for?

The Pythagorean Theorem Calculator is designed to find the length of a missing side in a right triangle using the Pythagorean Theorem formula.

#### Are there any restrictions on input values?

While the calculator is designed to handle a wide range of values, extremely large numbers might result in computational delays or errors.

#### Can I save or export the results?

The calculator provides results on the screen.

#### What is the Pythagorean Theorem?

The Pythagorean Theorem is a fundamental theorem in geometry that states that, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.