Question

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

Explanation:

Step1: Identify the problem type

It's a right - triangle side - length problem, use Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse.

Step2: Determine the hypotenuse

Since 15 is the longest side, let $c = 15$, and $a = 13$. We want to find $b$.

Step3: Rearrange the Pythagorean theorem

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

Step4: Substitute the values

$b=\sqrt{15^{2}-13^{2}}=\sqrt{(15 + 13)(15 - 13)}=\sqrt{28\times2}=\sqrt{56}$.

Step5: Calculate and round

$\sqrt{56}\approx7.5$.

Answer:

$7.5$