Q18 of 35 Page 219

From the top of a building , 60 m high, the angles of depression of the top and bottom at a vertical lamp post are observed to have measure 30 and 60 respectively. Find,

(1) the horizontal distance between building and lamp post.


(2) the height of the lamp post.


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

Let AB be the building and CD be the lamppost.



The height of the building AB = 60 m


Horizontal line DE intersects AB in E.


Let BE = CD = x


AE = AB – BE = (60 – x) m


∠AED = ∠ABC = 90⁰


Now, the angle of depression of the top D and then bottom C of the post CD are 30⁰ and 60⁰ respectively from A.


Then, ∠ADE = ∠XAD = 30⁰ and


∠ACB = ∠XAC = 60⁰


In ∆ADE,




DE = √3(60 – x) ………(1)


In ∆ABC,




…………..(2)


Now, BC = DE


From (1) and (2),


√3(60 – x) = 20√3


60 – x = 20


X = 40


1) The horizontal distance between the building and the lamppost


= BC


= √3(60 – x)


= √3(60 – 40)


= 20√3


= 20 × 1.73


= 34.6


2) The height of the lamppost


= CD


= x


= 40 m


3) The difference between the heights of the building and the lamppost


= AB – BE


= 60 – x


= 60 – 40


= 20 m


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