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Two poles of equal heights are standing opposite to each other on either side of the road, which is 120 feet wide. From a point between them on the road,

the angles of elevation of the top of the poles are 60 degres and 30 degrees respectively. Find the height of the poles and the distances of the point from the poles



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See diagram.

AD and BC are the poles of height H.
     AP + PB = 120 feet
  => H Cot 60 + H Cot 30 = 120 feet              
  =>  H /√3 + H √3 = 120 feet
  => H = 30 √3  feet

Distances of the point from the poles:
        AP = H COt 60 =  30 feet
       BP = H Cot 30  =  30 √3 feet

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