Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 9.2$ cm and one - leg be $b = 8.9$ cm. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$a=\sqrt{9.2^{2}-8.9^{2}}=\sqrt{(9.2 + 8.9)(9.2 - 8.9)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $9.2+8.9 = 18.1$ and $9.2 - 8.9=0.3$. Then $a=\sqrt{18.1\times0.3}=\sqrt{5.43}$.

Step3: Calculate the square root and round

$a=\sqrt{5.43}\approx2.3$ cm.

Answer:

$2.3$