Question

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

Explanation:

Step1: Identify the type of triangle

It is a right - triangle. Let the hypotenuse $c = 25$ and one side $a = 22$. We use the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, and we want to find $b$.

Step2: Rearrange the Pythagorean theorem

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

Step3: Substitute the values

Substitute $c = 25$ and $a = 22$ into the formula: $b=\sqrt{25^{2}-22^{2}}=\sqrt{(25 + 22)(25 - 22)}=\sqrt{47\times3}=\sqrt{141}$.

Step4: Calculate the value

$\sqrt{141}\approx11.9$.

Answer:

$11.9$