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Question

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=tan60ABBO=3BO=AB3
In ΔCDO
CDDO=tan30CD150BO=13CD3=150AB3CD3+AB3=150
Since the poles are of equal heights
therefore AB=CD
So,
CD(3+13)=150CD(3+13)=150CD(43)=150CD=37.53
BO=AB3=CD3=37.533=37.5DO=BDBO=15037.5=112.5
Hence the height of poles are 37.53 and the distance of point O from either of the poles is 37.5m and 112.5m

1061687_1149419_ans_722410a3b9f94e08afc749ae0035643a.png

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