Anonymouslizard
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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

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 harb class=

Respuesta :

LammettHash

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

Now use the law of cosines: it says [tex]d[/tex] satisfies

[tex]d^2=16^2+18^2-2(16)(18)\cos145^\circ[/tex]

and solving for [tex]d[/tex] gives

[tex]d=\sqrt{16^2+18^2-2(16)(18)\cos14^\circ}\implies d\approx32[/tex]

so the answer is C.

Answer: The answer is C.

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