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, $c = 97$ cm and $b = 72$ cm. We need to find $a$. Rearranging the formula gives $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$a=\sqrt{97^{2}-72^{2}}=\sqrt{(97 + 72)(97 - 72)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $97+72 = 169$ and $97 - 72 = 25$. Then $a=\sqrt{169\times25}$. Since $\sqrt{169\times25}=\sqrt{169}\times\sqrt{25}$, and $\sqrt{169}=13$, $\sqrt{25}=5$, so $a = 13\times5=65$ cm.

Answer:

65