# 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.

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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