Question

A 6 ft man finds the angle of elevation of a 24 ft tall tower and the angle of depression of its base are complimentry angles. The distance of the man from the pillar is

Answer 1

as both the angles are complimentary 
so, let angle of depression is α
the angle of elevation = 90°- α
x= distance between man and pillar
tanα = 6/x
and also tanα = x/18
comparing both,
6/x= x/18
⇒x²= 18×6
⇒x = 6√3 ft 
see the figure attached