Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here $c = 50$ m and $b=14$ m, and we want to find $a$. So, $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$a=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $a=\sqrt{64\times36}=\sqrt{2304}$.

Step3: Calculate the square - root

$a = 48$ m

Answer:

48