# Right Triangle Calculator

Right Triangle Calculator is used in checking if the measurements of the three given sides form a right triangle. The Pythagoras Theorem gives the relation between the sides of a right triangle. It is used to determine if the given side lengths will form a right triangle or not.

## What is Right Triangle Calculator?

Right Triangle Calculator is an online tool that assists in verifying whether a right triangle can be formed by the given side lengths. For a triangle to be a right triangle the three sides should form a Pythagorean Triple. This implies that the Pythagoras Theorem must be satisfied. To use the* right triangle calculator *enter the values in the input boxes.

## How to Use Right Triangle Calculator?

Please follow the below steps to verify whether the given triangle is a right triangle using the online right triangle calculator.

**Step 1:**Go to Cuemath's online right triangle calculator.**Step 2:**Enter the values in the input boxes of the right triangle calculator**Step 3:**Click on the**"Calculate"**button to find if the sides form a right triangle.**Step 4:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How Does Right Triangle Calculator Work?

The Pythagoras theorem states that the square of the hypotenuse is equal to the sum of squares of the altitude and the base. The hypotenuse forms the longest side of the right triangle. It is the side opposite to the angle that measures 90 degrees. For a triangle to be classified as a right triangle it needs to satisfy the Pythagoras Theorem. We can use the following steps to determine if the sides form a right triangle.

- Take the square of the longest side or hypotenuse.
- Take the square of the remaining two sides and add them.
- If the values in step 1 and step 2 are the same, the triangle will form a right triangle. This implies that the Pythagoras theorem is satisfied. It also indicates that the three sides form a Pythagorean Triple.
- If the values in step 1 and step 2 are different, the triangle is not a right triangle.

The formula for the Pythagoras Theorem is given below:

Hypotenuse^{2} = Altitude^{2 }+ Base^{2}

## Solved Examples on Right Triangle

**Example 1:** Find if (3, 4, 5) forms a right triangle and verify it using the online right triangle calculator.

**Solution:**

Hypotenuse = 5

Base = 3

Altitude = 4

According to the Pythagoras Theoream

Hypotenuse^{2} = Altitude^{2 }+ Base^{2}

^{2}= 25

Sum of squares of altitude and base = 3^{2} + 4^{2} = 25

As these values are the same thus, the triangle is a right triangle.

**Example 2:** Find if (1, 2, 3) forms a right triangle and verify it using the online right triangle calculator.

**Solution:**

Hypotenuse = 3

Base = 1

Altitude = 2

According to the Pythagoras Theorem

Hypotenuse^{2} = Altitude^{2 }+ Base^{2}

^{2}= 9

Sum of squares of altitude and base = 1^{2} + 2^{2} = 5

As these values are not the same thus, the triangle is not a right triangle.

Now using the online right triangle calculator find if the following form a right triangle or not.

- (5, 12, 13)
- (8, 7, 14)

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