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

Answer:

32.0

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs. Here $c = 40$ cm and $b = 24$ cm, and we want to find $a$. So $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$a=\sqrt{40^{2}-24^{2}}=\sqrt{(40 + 24)(40 - 24)}$ (using $x^{2}-y^{2}=(x + y)(x - y)$). Then $a=\sqrt{64\times16}=\sqrt{1024}$.

Step3: Calculate the square - root

$a = 32$ cm. Since we are asked to round to the nearest tenth, $a=32.0$ cm.