From the top of the tower 24 m high the angle of depression of the top and foot of the pole are observed to be 45degree and 60degree respectively find the height of the pole

Answer 1

As always, draw the diagram. You can see that to find h, you just use
24/(h-24) = tan60°

Answer 2

label the top of the tower as A, label the top of the pole as P and its bottom as Q.
draw a horizontal from A to hit PQ at B.
BQ = 24
in triangle ABQ, tan60 = 24/AB
AB = 24/tan60

in triangle ABP
tan45 = BP/(24/tan60)
BP = (24/tan60)(tan45 ) = .....