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Question
The vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is
30 and that of the top of the flagstaff 60 . Find the height of the tower
[Use `sqrt(3)` 1.732 ]
Solution
Let AB be the tower and BC be the flagstaff,
We have,
BC = 6m, ∠AOB = 30° and ∠AOC - 60°
Let AB = h
In ΔAOB
`tan 30° = (AB)/(OA)`
`⇒ 1/ sqrt(3) = h/( OA)`
` ⇒ OA = h sqrt(3)` ..............(i)
Now in Δ AOC,
` tan 60° = (AC)/(OA)`
`⇒ sqrt(3) = (AB +BC)/ (h sqrt(3))` [ Using (i)]
⇒ 3h = h + 6
⇒ 3h - h = 6
⇒ 2h = 6
`⇒ h= 6/2`
⇒ h = 3m
So, the height of the tower is 3 m.
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