Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, $c = 9.2$ cm and $b = 8.9$ cm. We want to find $a$, 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

$a\approx2.3$ cm (rounded to the nearest tenth).

Answer:

$2.3$