Question

winchester is 5.2 miles due north of the airport, and springtown is due east of the airport. if the distance between winchester and springtown is 9.1 miles, how far is springtown from the airport? if necessary, round to the nearest tenth.

Explanation:

Step1: Recognize right - triangle

The positions of Winchester, Springtown and the airport form a right - triangle. Winchester is 5.2 miles north of the airport and the distance between Winchester and Springtown is 9.1 miles. Let the distance between Springtown and the airport be $x$.

Step2: Apply Pythagorean theorem

According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 9.1$ (the hypotenuse, distance between Winchester and Springtown) and $a = 5.2$ (distance between Winchester and the airport), and $b=x$. So $x=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $c = 9.1$ and $a = 5.2$ into the formula: $x=\sqrt{9.1^{2}-5.2^{2}}=\sqrt{(9.1 + 5.2)(9.1 - 5.2)}=\sqrt{14.3\times3.9}=\sqrt{55.77}\approx7.5$.

Answer:

7.5