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 $c = 17$ mm and $a = 15$ mm. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{17^{2}-15^{2}}=\sqrt{(17 + 15)(17 - 15)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{(32)\times(2)}=\sqrt{64}$.

Step3: Calculate the square root

$b = 8$ mm.

Answer:

8