Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if b = 72 miles and c = 97 miles, what is a? if necessary, round to the nearest tenth.
a = miles

Explanation:

Step1: Apply Pythagorean theorem

According to the Pythagorean theorem, $a^{2}+b^{2}=c^{2}$. We can rewrite it to find $a$ as $a = \sqrt{c^{2}-b^{2}}$.

Step2: Substitute given values

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

Answer:

65