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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.
