Question

As shown in the diagram, a ship sails 16 nautical miles east from a harbor. It then sails 18 nautical miles in the direction of N 55° E. How far is it from the harbor to the nearest nautical mile?
A) 11 nautical miles
B) 24 nautical miles
C) 32 nautical miles
D) 36 nautical miles

Answer 1

The angle between the legs of length 16 and 18 has measure 90 + 55 = 145 degrees.

Now use the law of cosines: it says $d$ satisfies

$d^2=16^2+18^2-2(16)(18)\cos145^\circ$

and solving for $d$ gives

$d=\sqrt{16^2+18^2-2(16)(18)\cos14^\circ}\implies d\approx32$

so the answer is C.