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Question
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]
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.
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