Q16 of 61 Page 215

From the top of a tower of height 60 m, the angles of depression of the top and the bottom of a building are observed to be 30° and 60° respectively. Find the height of the building.


Here, AB is tower and EC is building.


Given, AB = 60 m and EC = ?


In triangle ABC,


Let AB = x


⇒ BD = 60 – x


And, ∠ ACB = ∠OAC (alternate angles are equal)


∠ACB = 30°


We know,





⇒ BC = x √3 ……… (1)


In triangle ADE,


∠ AED = ∠OAE (alternate angles are equal)


∠AED = 60°





……… (2)


∵ BC = DE


⇒ equation (1) = equation (2)



⇒ 3x = 60


⇒ x = 20 m


∵ CE = BD and BD = 60–x.


⇒ CE = 60 – 20 = 40 m


∴ Height of the building = 40 m.


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