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Pythagorean Theorem

Introduction

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

Pythagorean Theorem example

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:

\( \displaylines{a^2+b^2=c^2 \\ 3^2+4^2=c^2 \\ 9+16=c^2 \\ c^2=25 \\ c=5} \) 

Therefore, the hypotenuse has a length of 5.

Example: