Question

from a top of a hill 200 high the angle of depression of the top and bottom of a pillar are30and and 60 resectively .find height of the pillar and its distance from the hill

Answer 1

Please refer to the given figure,
AD = BC = 200m
BE = 200-EC
Tan 30° = BE/AB
     1/√3 = 200-EC/AB
         AB=√3(200-EC) (1)
Tan 60° = BC/AB
Putting the value of AB we get,
Tan 60° = 200/√3(200-EC)
3(200-EC) = 200
  600-3EC = 200
         3EC = 400
           EC = 133.33
Height of the tower = 133.33m
Now, Tan 60° = BC/AB
                 √3 = 200/AB
                 AB = 200/√3
                       =115.47
Distance between pillar and hill = 115.47m