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

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