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Geometry

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Trigonometry: Law of Sines/Application/Ship at Sea

GEOM-NXLHNW

A ship is sighted at sea between two observation points along the New England coastline that are $40.5$ miles apart. The angle formed by the coastline and the line between the ship and the first observation point measures ${35.4}^{\circ}$. The angle formed by the coastline and the line between the ship and the second observation point measures ${55}^{\circ}$.

What is the difference in the distance between the first observation point and the ship and the second observation point and the ship?

A

$7.32$ miles

B

$9.72$ miles

C

$17.04$ miles

D

$56.64$ miles