# How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 8, C= 16?

Apr 12, 2018

The missing side of the right triangle is $\sqrt{192}$

#### Explanation:

The formula for the Pythagorean Theorem is ${a}^{2} + {b}^{2} = {c}^{2}$

You are given a=8 and c=16 so plug those numbers into the formula:

${8}^{2} + {b}^{2} = {16}^{2}$

$64 + {b}^{2} = 256$

Subtract 64 from both sides

${b}^{2} = 192$

Square root both sides to get rid of the exponent

$\sqrt{{b}^{2}} = \sqrt{192}$

$b = \sqrt{192}$

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To simplify $\sqrt{192}$ :

Factor 64 out of 192

$\sqrt{64 \left(3\right)}$

Rewrite 64 as ${8}^{2}$

$\sqrt{{8}^{2} \cdot 3}$

Pull terms out from under the radical

$8 \sqrt{3}$

The result can be shown in both exact and decimal forms.

Exact Form:
$8 \sqrt{3}$

Decimal Form:
13.856406456 . . .