Option A: The vessel has sailed 34 miles South
Explanation:
Given that the vessel sails 41 miles S 35° E.
We need to determine the how far south the vessel has sailed.
Let us use the Pythagorean theorem to find the distance of the vessel has sailed.
Thus, we have,
[tex]cos \ \theta=\frac{adj}{hyp}[/tex]
Substituting [tex]\theta=35^{\circ}[/tex] , [tex]adj=x[/tex] and [tex]hyp=41[/tex]
Hence, we get,
[tex]cos \ 35=\frac{x}{41}[/tex]
Simplifying, we have,
[tex]0.82=\frac{x}{41}[/tex]
Multiplying both sides by 41, we have,
[tex]33.62=x[/tex]
Rounding off to the nearest integer, we have,
[tex]34=x[/tex]
Thus, the vessel has sailed 34 miles South.
Therefore, Option B is the correct answer.
