Answer :

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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