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, $c = 8.8$ ft and $a = 8.3$ ft. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{8.8^{2}-8.3^{2}}=\sqrt{(8.8 + 8.3)(8.8 - 8.3)}$ (using $x^{2}-y^{2}=(x + y)(x - y)$). First, $8.8+8.3 = 17.1$ and $8.8 - 8.3=0.5$. Then $b=\sqrt{17.1\times0.5}=\sqrt{8.55}$.

Step3: Calculate the square - root

$b=\sqrt{8.55}\approx2.9$ ft.

Answer:

$2.9$