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

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse $c = 200$ mm and one - leg $a = 96$ mm. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{200^{2}-96^{2}}=\sqrt{(200 + 96)(200 - 96)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{296\times104}=\sqrt{30784}=175.45$.

Step3: Round to the nearest tenth

$b\approx175.5$ mm.

Answer:

$175.5$