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

Answer:

65.0

Explanation:

Step1: Apply Pythagorean theorem

$c^{2}=a^{2}+b^{2}$, where $c = 97$ (hypotenuse) and $b = 72$. We want to find $a$. So, $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$a=\sqrt{97^{2}-72^{2}}=\sqrt{(97 + 72)(97 - 72)}=\sqrt{169\times25}$.

Step3: Calculate square - roots

$\sqrt{169\times25}=\sqrt{169}\times\sqrt{25}=13\times5 = 65$. Since we are asked to round to the nearest tenth, the answer is $65.0$.