As you draw your equation into a triangle ;the <A=220°, __a__ small is 150 miles which we place to the opposite of the angle .THE <C=130°,__c__ small is 130 miles which we place into the opposite of the angle. and the <B is unknown and its small one.

as we solve it:

to get the <B follow the formula of A+B+C=180° so we just only need the <B coz we the <A <C. <B=180°-220°-130° =<B is -170° it cannot be because no negative dimension.as the question needed just the shortest distance.

solve:

sin A/ a=sin B/ b=sin C/c

sin 220° /150 miles= sin 130°/ 130 miles= sin -170° /c

sin 220° /150 miles=sin -170° /c; make it cross multiply.

c=150 miles(sin -170°)/(sin 220°); do it in a calculator.

c=40.52 miles; round to nearest tens.