Question

what is the length of the missing leg? if necessary, round to the nearest tenth. b = meters

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs. Here $c = 95$ m and $a = 57$ m. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{95^{2}-57^{2}}=\sqrt{(95 + 57)(95 - 57)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, $95+57 = 152$ and $95 - 57=38$. Then $b=\sqrt{152\times38}=\sqrt{5776}$.

Step3: Calculate square root

$\sqrt{5776}=76$ m.

Answer:

76