Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the sides of the right - triangle be $a$, $b$, and $c$ where $c$ is the hypotenuse. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. If one leg is $a = 23$ and the hypotenuse $c = 30$, we want to find the other leg $b$. Rearranging the formula gives $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 23$ and $c = 30$ into the formula: $b=\sqrt{30^{2}-23^{2}}=\sqrt{900 - 529}=\sqrt{371}$.

Step3: Calculate and round

$\sqrt{371}\approx19.3$.

Answer:

$19.3$