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

Question

3219 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-12T13:27:41

The missing side of the right triangle is $\sqrt{192}$ $sqrt192$

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

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

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

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

Subtract 64 from both sides

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

Square root both sides to get rid of the exponent

$\sqrt{b^{2}} = \sqrt{192}$ $sqrt(b^2) = sqrt192$

$b = \sqrt{192}$ $b = sqrt192$

$- - - - - - - - - -$ $----------$

To simplify $\sqrt{192}$ $sqrt192$ :

Factor 64 out of 192

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

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

$\sqrt{8^{2} \cdot 3}$ $sqrt(8^2 * 3)$

Pull terms out from under the radical

$8 \sqrt{3}$ $8sqrt3$

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

Exact Form:
$8 \sqrt{3}$ $8sqrt3$

Decimal Form:
13.856406456 . . .