Question

From the top of a 210 foot lighthouse located at sea level, the keeper spots a boat at an angle of depression of 23 degrees

Answer 1

The distance from the lighthouse to the boat will be given by:
tan θ=opposite/adjacent
θ=angle of depression=23
opposite= height of the lighthouse
adjacent=distance from the boat to the bottom of the light house
hence
tan 23=210/a
thus solving for a we obtain:
a=210/tan23
hence
a=494.73 ft