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The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45 . If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60 , then find the height of the flagstaff [Use `sqrt(3)` 1.732]

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#### Solution

Let BC and CD be the heights of the tower and the flagstaff, respectively.

We have,

AB = 120m, ∠BAC = 45º ,∠BAD = 60°

Let CD = x

In ΔABC,

`tan 45° = (BC)/(AB)`

`⇒ 1 =(BC)/120`

`⇒ BC = 120m`

Now , in ΔABD,

` tan 60º (BD )/(AB)`

`⇒ sqrt(3)= (BC +CD)/ 120`

`⇒ BC + CD = 120 sqrt(3)`

`⇒ x = 120 sqrt( 3 )-120`

`⇒ x = 120 ( sqrt(3)-1)`

⇒ x = 120 ( 1.732 -1)

⇒ x = 120 (0.732)

`⇒ x = 87.84 ~~ 87.8m`

So, the height of the flagstaff is 87. 8 m.

Concept: Heights and Distances

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