Q29 of 49 Page 1

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60o and 30o respectively. Find the height of the poles and the distances of the point from the poles.

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Let AB = DE = y m be the two poles such that BD = 80 m.


Let CD = x m


∴ BC = (80 – x) m


In Δ CDB,


tan 30° = BD/CD


⇒ 1/√3 = y/x


∴ x = √3y ....(1)


In Δ CBA,


tan 60° = AB/BC


⇒ √3 = y/(80-x)


⇒ √3(80-x) = y


⇒ √3(80-√3y) = y [from(1)]


⇒ 80√3-3y = y


⇒ 4y = 80√3


∴ y = 20√3 m


Substituting the value of y in equation (1), we get-


x = 60 m


Hence, Height of each pole = 20√3 m


and, Distance between the poles = 60 m.


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