Question

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 be $c = 8.3$ mm and one - leg be $b = 3.1$ mm. The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, so $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

Substitute $c = 8.3$ and $b = 3.1$ into the formula: $a=\sqrt{8.3^{2}-3.1^{2}}=\sqrt{(8.3 + 3.1)(8.3 - 3.1)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $8.3+3.1 = 11.4$ and $8.3 - 3.1 = 5.2$. Then $a=\sqrt{11.4\times5.2}=\sqrt{59.28}$.

Step3: Calculate the square root

$a=\sqrt{59.28}\approx7.7$ mm.

Answer:

$7.7$