### What is a hypotenuse?

Ahead of discussing how to calculate the length of the hypotenuse, let us define it. The word hypotenuse comes from a Greek word hypoteinousa which means ‘stretching under’. The hypotenuse is the longest side of a right angled triangle and is opposite to the right angle.

### Formula to Calculate the Length of the Hypotenuse.

The method below is known as the Pythagorean theorem. Whereby, to find the hypotenuse of the triangle, you square(multiply a number by itself) the base (a²) and the height (b²) and then add them together to get the square of the hypotenuse (c²). Then find the square root of ‘c²’ to get the length of the hypotenuse.

**Example 1:**

Calculate the hypotenuse of the following right angled triangle.

Therefore , the hypotenuse of the triangle is 5 cm.

**Example 2:**

Suppose you are asked to find the length of a flight of stairs. If the distance between the floor and the top step is 12 feet and the distance from the wall to the lowest step is 9 feet.

The distance from the floor to the top step can be also called as the height and it is equal to 12feet.

The distance from the wall to lowest step can be also called the base, and it is 9 feet.

The length of flight of stairs is the hypotenuse. Therefore.

**Hypotenuse ^{2} = 12^{2}**

**+**

**9**

^{2}**= 144 + 81**

**Hypotenuse ^{2}= 225**

**Hypotenuse** **= √225**

Hence the length of the flight of stairs is 15 feet.