Two pillars of equal height and stand on either side of a roadway which is 150 m wide. At a point in the roadway between the pillars, the angle of elevation of the top of pillars are 600and 300. then find height of pillars-
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Solution
Let us consider the CD and AB are the poles and O is the point where elevation angle is made.
In ΔABO
ABBO=tan60∘ABBO=√3BO=AB√3
In ΔCDO
CDDO=tan30∘CD150−BO=1√3CD√3=150−AB√3CD√3+AB√3=150
Since the poles are of equal heights
therefore AB=CD
So,
CD(√3+1√3)=150CD(3+1√3)=150CD(4√3)=150CD=37.5√3
BO=AB√3=CD√3=37.5√3√3=37.5DO=BD−BO=150−37.5=112.5
Hence the height of poles are 37.5√3 and the distance of point O from either of the poles is 37.5m and 112.5m