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Question
The angle of elevation of the top of a tower at a point on the ground is 30º. What will be the angle of elevation, if the height of the tower is tripled?
Solution
Let the height of the tower AB be h units.
Suppose C is a point on the ground such that ∠ACB=30°
In right ∆ACB,
`tan 30°= (AB)/(AC)`
`⇒ 1/sqrt3=h/(AC)`
`⇒ AC=sqrt3h` ................(1)
Let the angle of elevation of the top of the tower at C be θ, if the height of the tower is tripled.
New height of the tower, AD = 3h units
In right ∆ACD,
`tan θ= (AD)/(AC)`
`⇒ tan θ =(3h)/(AC) `
`⇒ tan θ= (3h)/sqrt(3h)=sqrt3` [from (1)]
`⇒ tan θ= tan 60°`
`⇒ θ=60°`
Hence, the required angle of elevation is 60º.
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