In the given right triangle, find the missing length to the nearest tenth given the base is 17 ft and height is 11ft?

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Answer 1 · 2017-01-13T04:36:19

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Because this is a right triangle we can use the Pythagorean theorem to solve this problem.

The Pythagorean theorem states:

$a^{2} + b^{2} = c^{2}$ $color(red)(a)^2 + color(blue)(b)^2 = c^2$

Where $a$ $color(red)(a)$ and $b$ $color(blue)(b)$ are the base and height.

Substituting the lengths from the problem we can solve for $x$ $x$ :

$17^{2} + 11^{2} = c^{2}$ $color(red)(17)^2 + color(blue)(11)^2 = c^2$

$289 + 121 = c^{2}$ $289 + 121 = c^2$

$410 = c^{2}$ $410 = c^2$

$\sqrt{410} = \sqrt{c^{2}}$ $sqrt(410) = sqrt(c^2)$

$20.2 = c$ $20.2 = c$

The missing length is 20.2.