Question

9.3 mi. a 6.4 mi. what is the length of the missing leg? if necessary, round to the nearest tenth. a = miles

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, $c = 9.3$ and $b = 6.4$, and we want to find $a$. So, $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$a=\sqrt{9.3^{2}-6.4^{2}}=\sqrt{(9.3 + 6.4)(9.3 - 6.4)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, $9.3+6.4 = 15.7$ and $9.3 - 6.4 = 2.9$. Then $a=\sqrt{15.7\times2.9}=\sqrt{45.53}$.

Step3: Calculate the square root

$a=\sqrt{45.53}\approx6.7$

Answer:

$6.7$