A ship travels 60 miles due east, then adjusts it's course 15° northward. After traveling 80 miles in that direction, how far is the ship from it's point of departure?

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Answer 1 · 2017-12-03T10:55:01

#138.82color(white)(88)#miles

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From the diagram we can see we need to find a.

Using the Cosine Rule:

#a^2=b^2+c^2-2bc*cos(A)#

Let #/_ A = 165^@# , #b=60 and c= 80#

#a^2=(60)^2+(80)^2-2(60)(80)*cos(165^@)#

#a^2=3600+6400-9600*cos(165^@)=19272.89#

#->=>a=sqrt(19272.89)=138.82color(white)(88)#miles