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.
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° =
On multiplying and dividing by √3, we get
BC = ⇒ 20√3
Therefore distance between building
and lamp post is 20√3 m
(ii) In ∆AED
tan 30° =
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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