Pythagorean theorem calculator is used to find out the length of a remaining side of a right-angle triangle with their parameter, area, alpha, beta, and altitude. Enter the required parameters and the tool will instantly show calculations.

## What Is Pythagorean Theorem?

This three-squares theorem is stated as;

**In any right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of those two sides that meet at a right angle.”**

## Pythagorean Theorem Formula:

With the help of a Pythagorean theorem calculator square root, you can find the length of the remaining side of a triangle with their leg’s length. The converse of the Pythagorean theorem can be written as an equation called the Pythagorean equation.

**c² = a² + b² **

Where;

- c = longest side of the triangle called the hypotenuse
- a and b = length of the other two sides of the triangle

You can also find out the central angle of a circle with the help of our __area of a sector calculator__.

## How To Apply Pythagorean Theorem?

Our Pythagorean theorem calculator with radicles is a single way to clarify endure side of a right-angled triangle. You can understand the calculation procedure for the missing side of the triangle by considering the Pythagorean theorem example.

### Example:

Suppose that a ladder against the wall makes the right angle that has the lengths of their two legs “a” and “b” are 6m, and 8m respectively. Calculate the longest side of the right-angled triangle with its other components.

#### Solution:

$$c = \sqrt{a^2 + b^2}$$

$$c = \sqrt{6^2 + 8^2}$$

$$c = \sqrt{36 + 64}$$

$$c = \sqrt{100}$$

**c = 10 **

$$\alpha = \sin^{-1}(\frac{a}{c})$$

$$\alpha = \sin^{-1}(\frac{6}{10})$$

$$\alpha = 57^\circ$$

**alpha = 1 rad**

$$\beta = \sin^{-1}(\frac{b}{c})$$

$$\beta = \sin^{-1}(\frac{8}{10})$$

$$\beta = 57^\circ$$

**beta = 1 rad**

$$\text{ area} = \frac{a \times b}{2}$$

$$\text{ area} = \frac{6 \times 8}{2}$$

$$\text{ area} = \frac{48}{2}$$

**area = 24 m^2**

$$\text{ Perimeter} = a + b + c$$

Perimeter = 6 + 8 + 10

**Perimeter = 24 **

$$\text{ h} = \frac{a \times b}{c}$$

$$\text{ h} = \frac{6 \times 8}{10}$$

$$\text{ h} = \frac{48}{10}$$

**h = 4.8**

Also try our __circumference calculator__ to find the area, diameter, and circumference online.

## Working Of Pythagorean Theorem Calculator:

Our Pythagorean solver is an efficient way to find the longest side of a right angle. Find the three sides length of Euclidean geometry with the help of the Pythagorean triangle calculator. Take a quick look at the inputs.

**Input:**

- Select the calculation menu
- Place the values according to the selection
- Select the unit in which you want your calculations
- Set the number of decimals according to your need
- Tap
**“calculate”**

**Output:**

Our Pythagoras calculator gives the following outputs after putting the values in the cells.

- The length of the unknown side
- Table to show the values of area, perimeter, ∠α, ∠β, and h will be given.
- Complete step-by-step calculations

## FAQs

### What Are The Limitations of The Theorem?

Pythagoras' theorem is only applicable in the case of the right-angled triangle. If there is another type of triangle, then this will not be applicable. It is valid for the 2-dimensional figures.

## References:

From the source **Wikipedia:** Pythagorean theorem, Proofs using constructed squares, Other proofs of the theorem, Converse, Consequences and uses of the theorem, Generalizations,

From the source **Khan Academy:** introduction to the Pythagorean Theorem, Pythagorean theorem example, right triangle side lengths, Use Pythagorean theorem to find isosceles triangle side lengths.