Q. 74.0( 4 Votes )

The angle of elevation of the top of a tower standing on a horizontal plane from a point C is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is
A.

B.

C.

D.

Answer :

Given: The angle of elevation of the top of a tower standing on a horizontal plane from a point C is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. 

To find: The height of the tower 

Solution:






Let h be the height of the tower on horizontal plane.


Let α be the angle of elevation from point C and β be the angle of elevation from point B


Given CB = d


In Δ PCB


tan (α) =


x =


In Δ CDB


tan(β) =


   

   


⇒ tanβ ( h - d tanα) = h tanα


⇒  h tanβ - d tan a tanβ = h tan a


⇒  h (tanβ – tan a) = d tan a tanβ





Use the formula:










Hence (b) is the answer.

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