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, $c = 7.5$ ft and $a = 6.5$ ft. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{7.5^{2}-6.5^{2}}=\sqrt{(7.5 + 6.5)(7.5 - 6.5)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $(7.5 + 6.5)(7.5 - 6.5)=(14)\times(1)=14$. Then $b=\sqrt{14}\approx3.7$ ft.

Answer:

$3.7$