A lighthouse standing on the top of a cliff is observed from two open boats (boats are not decked over) A and B in a vertical plane through the light house. The angle of elevation of the top of the lighthouse viewed from B is 16 degrees and the angles of elevation of the top and bottom viewed from A are 40 degrees and 23 degrees respectively. If the boats are 1320 ft. apart, find the height of the lighthouse and the height of the cliff.

Answer 1

c = cliff height
h = lighthouse hight
a = distance of A from cliff
b = distance of B from cliff

c/a = tan 23°
(c+h)/a = tan 40°
(c+h)/b = tan 17°

So, clearing fractions and plugging in the trig values, we have

c = .4245a
c+h = .8391a
c+h = .3057b
b = a+1320

h = 313.65
c = 321.14