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