Pythagorean Theorem

Introduction

Suppose that we have a right-angled triangle (a triangle that contains a 90^o angle) as shown below, where c is the side opposite the right angle (this side c is called the “hypotenuse”)

The Pythagorean Theorem tells us that the lengths of the sides are related by the following formula: a² + b² = c² 

Example:

If a right-angled triangle has one side of length 3 and one side of length 4, find the length of the hypotenuse.

Solution:

a² + b² = c² 

3² + 4² = c² 

9 + 16  = c²

         c² = 25

           c = 5

Therefore, the hypotenuse has a length of 5.

Example: