An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 4° and θ = 8.5° How far apart are the ships?
+37101 We'll have to assume the ships and the base of the tower form a straight line. (Maybe that's what 'directly offshore ' implies)
theta ship distance from lighthouse would be defined by tan (theta) = tan 8.5= 350 /x yields x = 2341.9 ft
Similarly Beta ship distance is tan(beta) = tan 4 = 350/x x = 5005.2 ft from lighthouse
the difference between these two distances is the distance between the ships
5005.2 - 2341.9 = 2663.3 ft
