A cruise ship travels 330 miles due east before turning 25 degrees north of east. It travels 180 miles along its new course. How far is the cruise ship from its initial position?

we know that
applying the law of cosines
c²=a²+b²-2*a*b*cos C

in this problem
a=330 miles
b=180 miles
c=-----> distance of the cruise ship from its initial position
C=180-25----> C=155°

see the attached picture to better understand the problem
c²=a²+b²-2*a*b*cos C----> c²=330²+180²-2*330*180*cos 155
c²=248969.37------> c=498.97 miles

the answer is
498.97 miles