Question

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, $c = 20$ mm and $a = 16$ mm. We need to find $b$. Rearranging the formula for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 20$ and $a = 16$ into the formula: $b=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{36\times4}=\sqrt{144}$.

Step3: Calculate the square root

$\sqrt{144}=12$

Answer:

12