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Question
The angle of elevation of a tower from a point 200 m from its base is θ, when `tan θ = 2/5`. The angle of elevation of this tower from a point 120m from its base is `Φ`. Calculate the height of tower and the value of `Φ`.
Solution
Let OT be the tower .
A and B be the two points from where the angle of elevation to the top of the tower is measured.
In ΔAOT,
`"OT"/"OA" = tanθ`
⇒ `"h"/200 = 2/5`
⇒ h = 80 ...(1)
Thus , the height of the tower is 80 m.
In ΔBOT,
`"OT"/"OB" = tanΦ`
⇒ `"h"/120 = tanΦ`
⇒ `80/120 = tanΦ` [Using (1)]
⇒ `2/3 = tanΦ`
From the table , we get `Φ = 34^circ`.
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