Question

1. there is a chick - fil - a exactly 6 miles due east of berkmar middle school. target is south of the middle school. from chick - fil - a the shortest distance to target is 10 miles. how far apart are the middle school and target? round to the nearest hundredth.

Explanation:

Step1: Identify the right - triangle

The positions of Berkmar Middle School, Chick - fil - a, and Target form a right - triangle. The distance from Berkmar Middle School to Chick - fil - a is one leg ($a = 6$ miles), the distance from Chick - fil - a to Target is the hypotenuse ($c = 10$ miles), and the distance from Berkmar Middle School to Target is the other leg ($b$).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We want to find $b$, so we can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 6$ and $c = 10$ into the formula:
\[

$$\begin{align*} b&=\sqrt{10^{2}-6^{2}}\\ &=\sqrt{100 - 36}\\ &=\sqrt{64}\\ &=8 \end{align*}$$

\]

Answer:

8.00