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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