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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