Question

find the length of the third side. if necessary, round to the nearest tenth. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse $c = 30$ and one - side $a = 18$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $b$ is the unknown side. We can rewrite it as $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 30$ and $a = 18$ into the formula: $b=\sqrt{30^{2}-18^{2}}=\sqrt{(30 + 18)(30 - 18)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{48\times12}=\sqrt{576}$.

Step3: Calculate the square - root

$\sqrt{576}=24$.

Answer:

24