From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. Find the height of the pole.
In the fig CE is the height of the pole and x be the distance between tower and pole.
In ∆ADE
tan 45° = 
1 = 
x = 50-h ----- (1)
In ∆ABC
tan 60° = 
√3 = 
x = 
-----(2)
On substituting value of x in eqn (1), we get
50 – h = 
h = 50 - 
⇒ 
⇒ 21.13m
Therefore the height of the pole is 21.13m
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