Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$, $b$ are the legs. Here, $c = 26$ ft and $b = 10$ ft. We want to find $a$, so $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

Substitute $c = 26$ and $b = 10$ into the formula: $a=\sqrt{26^{2}-10^{2}}=\sqrt{(26 + 10)(26 - 10)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $(26 + 10)(26 - 10)=(36)\times(16)=576$. Then $a=\sqrt{576}$.

Step3: Calculate the square root

$\sqrt{576}=24$.

Answer:

24