Question

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

Explanation:

Step1: Identify the Pythagorean theorem

For a right - triangle with hypotenuse $c$ and legs $a$ and $b$, $a^{2}+b^{2}=c^{2}$. Here, $c = 16$ and $a = 11$, and we want to find $b$.

Step2: Rearrange the formula

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

Step3: Substitute the values

$b=\sqrt{16^{2}-11^{2}}=\sqrt{256 - 121}=\sqrt{135}$.

Step4: Calculate the square - root and round

$\sqrt{135}\approx11.6$.

Answer:

$11.6$