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A ship sailing parallel to shore sights a lighthouse at an angle of 14° from its direction of travel. After traveling 4 miles farther, the angle is 23°. At that time, how far is the
nip from the lighthouse? Round your answer to two decimal places as needed.
A. 4.00 mi
B. 2.48 mi
C. 6.19 mi
D. 9.99 mi
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sqdancefan

Answer:

  C.  6.19 mi

Step-by-step explanation:

The angle between the two ship locations as viewed from the lighthouse is ...

  23° -14° = 9°

This is opposite the known side of the triangle: 4 miles. The unknown side, the distance to the lighthouse from the second position, is opposite the 14° angle in the triangle. The Law of Sines can be used to find the distance (d) of interest:

  d/sin(14°) = (4 mi)/sin(9°)

  d = (4 mi)(sin(14°)/sin(9°)) ≈ 6.1859 mi

The ship is 6.19 miles from the lighthouse at the second sighting.

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