# Pottersville is 51 miles south of Dubuque. Westview is 60 miles west of Dubuque. How far apart are Pottersville and Westview?

Feb 21, 2016

From Pottersville to Westview is about $78.75$ miles.

#### Explanation:

We know that Pottersville, or $P$ is $51$ miles south of Dubuque, or $D$, and that Westview ($W$) is $60$ miles west of Dubuque. I want to look at this more visually, so let's set it up:

$\textcolor{w h i t e}{\ldots \ldots} 60$ miles
$W$-----------$D$
$\textcolor{w h i t e}{.}$\color(white)(...........)| color(white)(.)color(white)(.)\color(white)(.........0)| color(white)(.)color(white)(..)\color(white)(.........)|color(white)(.)51 miles
$\textcolor{w h i t e}{.}$$\textcolor{w h i t e}{30.}$\color(white)(0000)| color(white)(.)color(white)(0330)\color(white)(333)| color(white)(.)color(white)(00000)\color(white)(33)| color(white)(.)color(white)(0000..)\color(white)(3)| color(white)(.)color(white)(3333333)$P$

By drawing the problem, we can see that this is a triangle. Now we can use Pythagoras formula, which is ${a}^{2} + {b}^{2} = {c}^{2}$.

This means that ${60}^{2} + {51}^{2} = {c}^{2}$, or $6201 = {c}^{2}$. The $\sqrt{6201} = 78.746$, which we'll round up to $78.75$. That means that the distance from Pottersville to Westview is $78.75$ miles.