what is the length of the missing leg? if necessary, round to the nearest tenth. b = millimeters

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, $c = 6$ mm and $a = 4$ mm. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{6^{2}-4^{2}}=\sqrt{36 - 16}=\sqrt{20}$.

Step3: Simplify and round

$\sqrt{20}=2\sqrt{5}\approx 4.5$ mm.

Answer:

$4.5$