Question

An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 7° and θ = 10.5° (see figure). How far apart are the ships? (Round your answer to one decimal place.) ft

Answer 1

the complete question in the figure attached

Let
x1------------------> distance  ship 1 from lighthouse
x2------------------> distance ship 2 from lighthouse

we know that
sin(θ)=350/x1   and  sin(β)=350/x2
x1=350/sin(θ)=350/sin(10.5)=1920.59 ft
x2=350/sin(β)=350/sin(7)=2871.93 ft

the answer are
distance ship 1 (x1)=1920.6 ft
distance ship 2 (x2)=2871.9 ft