Q. 234.4( 27 Votes )

The shadow of a tower standing on level ground is found to be 40 m longer when Sun’s altitude is 30° than when it was 60°. Find the height of the tower.

Answer :


Let the height of tower = h (m)
Since the tower is vertical to the ground.
∠ABC = 90°
We know, in a right-angle triangle,


In ∆ABC,


=


=


√3h = 40 ---------------(1)


In ∆ABD,


√3 =


h =√3 -------(2)


on substituting the value of h from eqn. (2) in eqn. (1)


h = √3× (√3h-40)


h = 3h-40√3


2h = 40√3


h = 20√3 m.


Therefore the height of the tower is 20√3 m.

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