# How do you use the Pythagorean Theorem to find the missing side of the triangle given: b = 5, c = 8?

Apr 19, 2016

If 8 is the hypotenuse than side $a = \sqrt{39}$

If 8 is not the hypotenuse than sude $a = \sqrt{89}$

#### Explanation:

You have not declared if the triangle is a right triangle ( has a 90 degree angle) nor have you declared if the side c is the hypotenuse or not. However, by including the use of Pythagoras you have implied it is a right triangle.

Let the unknown side be labeled $a$

$\textcolor{b l u e}{\text{Assumption 1: It is a right triangle and 8 is the hypotenuse}}$

$\implies {a}^{2} = {8}^{2} - {5}^{2} \text{ " =" " 64-25" "=" } 39$

$a = \sqrt{39}$

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$\textcolor{b l u e}{\text{Assumption 2: It is a right triangle and 8 is not the hypotenuse}}$

$\to {a}^{2} = {8}^{2} + {5}^{2} = 89$

$\implies a = \sqrt{89}$