Q50 of 68 Page 9

The angles of depression of the top and the bottom of a 7 m tall building from the top of a tower are 45° and 60° respectively. Find the height of the tower.


Let building be AB and tower be CD


The height of building, AB = 7 m


Let the height of tower = CD


and, the distance between tower and building = AC


The angle of depression to top of the building, ∠QDB = 45°


Angle of depression to bottom of building, ∠QDA = 60°


In the right Δ BDP, we have




⇒ BP = DP …(i)


In the right Δ ADC, we have




[∵ AC = BP]




∵ CD = DP + PC


⇒ CD = DP + AB [∵ AB = PC]


⇒ CD = DP + 7










⇒ CD = 16.56 (approx.)


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