Question

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

Explanation:

Step1: Identify the triangle type

It's a right - triangle. Use Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, assume the hypotenuse $c = 25$ and one side $a = 7$.

Step2: Apply the Pythagorean theorem

We want to find the other side $b$. Rearranging the formula gives $b=\sqrt{c^{2}-a^{2}}$. Substitute $c = 25$ and $a = 7$ into the formula: $b=\sqrt{25^{2}-7^{2}}=\sqrt{(25 + 7)(25 - 7)}=\sqrt{32\times18}=\sqrt{576}$.

Step3: Calculate the value of $b$

$\sqrt{576}=24$.

Answer:

24