Question

The angle of depression of the top and bottom of a tower as seen from the top of a 100m high cliff are 30degree and 60degree respectively. find the height of the tower

Answer 1

I assume you made a sketch.
On mine I let the distance between tower and cliff be x m
then tan60° = 100/x
x = 100/tan60°

In my smaller right-angled triangle at the top of my diagram ,
let the difference between height of tower and height of cliff be h
then tan 30 = h/x
h = xtan30
= (100/tan60)tan30

then height of tower = 100 - h

I will let you do all that button-pushing,
let me know what you got

Answer 2

99.99