Question

find the length of the missing side.

Explanation:

Step1: Identify the hypotenuse and given sides

The hypotenuse $c = 50$ in and one - side $a = 14$ in. We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $b$ is the missing side.

Step2: Rearrange the Pythagorean theorem

We get $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values

$b=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{64\times36}=\sqrt{64}\times\sqrt{36}=8\times6 = 48$ in.

Answer:

48 in.