Two lighthouses are located 25 miles from one another on a north-south line. If a person on a buoy is spotted 10° south of east from the

Question

Two lighthouses are located 25 miles from one another on a north-south line. If a person on a buoy is spotted 10° south of east from the northernmost lighthouse and 25° north of east from the southernmost lighthouse, how much closer is the closest lighthouse to the person on the buoy?

Answer 1

Draw and label a diagram.

N at the north lighthouse, S at the south lighthouse, B at the buoy.

∠SNB = 80°, ∠NSB = 65°, ∠NBS = 35°

 

Use the Law of Sines to determine NB and BS.