Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here $c = 41$ ft and $a = 9$ ft. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{41^{2}-9^{2}}=\sqrt{(41 + 9)(41 - 9)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, $41+9 = 50$ and $41 - 9=32$. Then $b=\sqrt{50\times32}=\sqrt{1600}$.

Step3: Calculate the square root

$\sqrt{1600}=40$

Answer:

$40$