Question

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

Explanation:

Step1: Identify right - triangle and apply Pythagorean theorem

Let the two given sides be $a = 10$ and $c = 24$. Assume the unknown side is $b$. In a right - triangle, $c^{2}=a^{2}+b^{2}$ (where $c$ is the hypotenuse). We need to solve for $b$. So, $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 10$ and $c = 24$ into the formula: $b=\sqrt{24^{2}-10^{2}}=\sqrt{(24 + 10)(24 - 10)}=\sqrt{34\times14}=\sqrt{476}$.

Step3: Calculate and round

$\sqrt{476}\approx21.8$.

Answer:

$21.8$