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:

#color(white)(......)60# miles

#W#-----------#D#

#color(white)(.)#\#color(white)(...........)|#
#color(white)(.)##color(white)(.)#\#color(white)(.........0)|#
#color(white)(.)##color(white)(..)#\#color(white)(.........)|##color(white)(.)51# miles

#color(white)(.)##color(white)(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.