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

Answer: The answer is C.

Answer 2

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=√(16^2+18^2-2(16)(18)\cos14^\circ)\implies d\approx32`

so the answer is C.