From the top of a lighthouse 55 ft above sea level, the angle of depression to a small boat is 11.3 degrees. How far from the foot of the lighthouse is the boat?

Let ##a## be the altitude of the lighthouse above sea level, ##a=55 ft## and ##b## the distance of the boat from the foot of the lighthouse, ##thetad = 11.3^0##

Solution:

##tan11.3^0 = 55/x##

##x = 55/(tan11.3^o) = 55/(0.19982)= 275.25 ft. ->Answer ##