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?

Question

11237 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-03T10:55:01

#138.82color(white)(88)#miles

enter image source here

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