The angles of depression of the top and bottom of a tower
Let the height of the tower be AB = h
Hence DE = h
Given height of the cliff, CD = 60Ö3 m
Hence CE = 60Ö3 – h
In right triangle AEC,
tan45° = CE/EA
1 = (60Ö3 – h )/EA
\ EA = 60Ö3 – h ----(1)
In right triangle CDB
tan60° = CD/DB
Ö3 = 60Ö3/DB
Hence DB = 60 m
That is EA = 60 m
Equation (1) becomes,
60 = 60Ö3 – h
h = 60Ö3 – 60 = 60(Ö3 – 1) m
Thus the height of the tower is 60(Ö3 – 1) m