How do you use the pythagorean theorem to solve for the missing side given a = 5, c = 19?

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Answer 1 · 2017-08-24T13:48:23

See a solution process below:

The Pythagorean Theorem states:"

$a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$

Where:

$a$ $a$ and $b$ $b$ are sides of a right triangle.

$x$ $x$ is the hypotenuse of the the right triangle.

Substituting and solving for $b$ $b$ gives:

$5^{2} + b^{2} = 19^{2}$ $5^2 + b^2 = 19^2$

$25 + b^{2} = 361$ $25 + b^2 = 361$

$25 - 25 + b^{2} = 361 - 25$ $25 - color(red)(25) + b^2 = 361 - color(red)(25)$

$0 + b^{2} = 336$ $0 + b^2 = 336$

$b^{2} = 336$ $b^2 = 336$

$\sqrt{b^{2}} = \sqrt{336}$ $sqrt(b^2) = sqrt(336)$

$b = \sqrt{336}$ $b = sqrt(336)$

$b = \sqrt{16 \cdot 21}$ $b = sqrt(16 * 21)$

$b = \sqrt{16} \cdot \sqrt{21}$ $b = sqrt(16) * sqrt(21)$

$b = 4 \sqrt{21}$ $b = 4sqrt(21)$

Or

$b = 18.330$ $b = 18.330$ rounded to the nearest thousandth.