Question:
Two pillars of equal heights are on the either sides of a road , which is 150 m wide.The angle of elevation of the top of the pillars are 60 and 30 degree resp. at a point on the road between the pillar. Find the height of each pillar
Answer:
Let the height of the equal pillars be AB = CD = h
Given, width of the road is 150 m
Let BE = x, the DE = 150 - x
In right angle triangle ABE,
tan 60 = h/x
=> √3 = h/x
=> h = √3x ............1
In right angle triangle CDE,
tan 30 = h/(150 - x)
=> 1/√3 = h/(150 - x)
=> √3h = 150 - x
=> √3h = 150 - h/√3 {from equation 1}
=> √3h + h/√3 = 150
=> (3h + h)/√3 = 150
=> 4h = 150√3
=> h = 150√3/4
=> h = 37.5√3 m
So, the height of the equal pillers is 37.5√3 m
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