Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 24$, one - leg be $a = 14$, and the other leg be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 24$ and $a = 14$ into the formula: $b=\sqrt{24^{2}-14^{2}}=\sqrt{(24 + 14)(24 - 14)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{(38)(10)}=\sqrt{380}$.

Step3: Calculate and round

$\sqrt{380}\approx19.5$.

Answer:

$19.5$