step 1
find the coordinates of the factory
the factory is 104 miles due north of the warehouse
the coordinates of the warehouse are (39,-52)
coordinates of the factory------> (39,-52+104)------> (39,52)
step 2
find the distance warehouse to airport
let
A coordinates of warehouse-------> A( 39,-52)
B coordinates of airport---------> B(-39,52)
C coordinates of factory-------> C(39,52)
distance AB=√[(52+52)²+(-39-39)²]------> distance AB=130 miles
step 3
find the distance airport to factory
B(-39,52)
C(39,52)
distance BC=√[(52-52)²+(39+39)²]-----> distance BC=39 miles
the total number of miles=distance AB+distance BC---> 130+39
the total number of miles=169 miles
<em>Thus</em> the answer is 169
