Q26 of 49 Page 1

The angle of elevation of the top of a building from the foot of the tower is 30 � and the angle of elevation of the top of the tower from the foot of the building is 60 �. If the tower is 60 m high, find the height of the building.

YGG.png

Let CD be the height of the building.


From fig-


In Δ ABD,


tan 60° = AB/BD


⇒ √3 = 60/BD


⇒ BD = 60/√3 = 20√3 m


Now, In Δ CDB


tan 30° = CD/BD


⇒ 1/√3 = CD/20√3


⇒ CD = 20 m


Thus, the height of the building is 20 m.


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