Q. 615.0( 7 Votes )

From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60° respectively. Find

(i) the horizontal distance between AB and CD.

(ii) the height of the lamp post.

(iii) the difference between the heights of the building and the lamp post.

Answer :

In the fig AB is the building of height 60m and CD is the lamp post of height h (m)


(i) In ∆ABC


tan 60° =


√3 =


BC =


On multiplying and dividing by √3, we get


BC = 203


Therefore distance between building


and lamp post is 20√3 m



(ii) In ∆AED


tan 30° =


=


= 20√3


AE = = 20


Therefore height of lamp post is CD = AB-AE 60-20 = 40 m


Therefore height of lamp post is 40 m


(iii) The difference between the height of the building and the lamp post is 60-40 = 20m


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