# Hypotenuse Calculator

Hypotenuse Calculator is a free online tool that helps to find the hypotenuse of a right-angled triangle. The hypotenuse is the longest side of a right triangle. Furthermore, it is the side opposite the right angle.

## What is a Hypotenuse Calculator?

Hypotenuse Calculator helps to calculate the hypotenuse of a right triangle with a given base and height. The Pythagoras Theorem is used to calculate the hypotenuse of a right triangle. To use the * hypotenuse calculator*, enter the values in the given input boxes.

### Hypotenuse Calculator

Note: Enter numbers up to 3 digits

## How to Use the Hypotenuse Calculator?

Follow the steps given below to find the hypotenuse of a right triangle using the hypotenuse calculator:

**Step 1:**Go to Cuemath's online Hypotenuse Calculator.**Step 2:**Enter the base and height of the triangle in the respective input boxes.**Step 3:**Click on the**"Calculate"**button to find the length of the hypotenuse.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Hypotenuse Calculator Work?

A triangle in which one angle measures 90 degrees and the remaining two angles are acute is known as a right-angled triangle or right triangle. The hypotenuse of a right triangle can be determined by the Pythagoras Theorem. This theorem gives the fundamental relationship between the three sides of a right triangle. It states that the sum of squares of the height and the base of a right triangle will be equal to the square of the hypotenuse. Moreover, the three sides of a right triangle are also known as Pythagorean triples. The formula for the Pythagoras theorem is given by:

Hypotenuse^{2} = (Base^{2} + Height^{2})

The steps to find the hypotenuse of a right triangle are given below:

- Step 1: Square the base and the height; Base
^{2}, Height^{2} - Step 2: Add the two values obtained in step 1; Base
^{2}+ Height^{2} - Step 3: Take the square root of the value from step 2 to get the length of the hypotenuse; Hypotenuse =
**√**(Base^{2}+ Height^{2})

## Solved Examples on Hypotenuse Calculator

**Example 1:** Find the hypotenuse of a right-angled triangle if its base is 3 units and height is 4 units. Verify it using the online hypotenuse calculator.

**Solution:**

Hypotenuse = **√**(Base^{2} + Height^{2})

= **√**(3^{2} + 4^{2})

= **√**25

= 5 units.

**Example 2:** Find the hypotenuse of a right-angled triangle if its base is 2.5 units and height is 3.2 units. Verify it using the online hypotenuse calculator.

**Solution:**

Hypotenuse = **√**(Base^{2} + Height^{2})

= **√**(2.5^{2} + 3.2^{2})

= **√**16.49

= 4.061 units.

Now, you can try the hypotenuse calculator to find the hypotenuse of the triangles with the following dimensions:

- Base = 7.2 units, Height = 15.6 units.
- Base = 23 units, Height = 47 units.

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