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