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To a man standing at the mid point of the line joining the feet of two vertical poles of same height. the angle of elevation of the tip of each pole is 300. When the man advances a distance of 40 metres towards one pole, the angle of elevation of the tip of this pole is 60°. What is the distance between the two poles ?
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- 120 metre
- 110 metre
- 130 metre
- 115 metre
- 120 metre
Correct Option: A
AB = CD = pole = h metre
BO = OD = x metre
OE = 40 metre ED = (x – 40) metre
In ∆OCD,
| tan 30°= | ||
| OD |
| ⇒ | = | ||
| √3 | x |
⇒ √3h = x ....(i)
In ∆CDE,
| tan 60° = | ||
| DE |
| ⇒ √3 = | ||
| x = 40 |
⇒ √3(x -40) = h
| ⇒ √3(x -40) = | ||
| √3 |
⇒ 3 (x – 40) = x
⇒ 3x – 120 = x
⇒ 2x = 120
⇒ x = 60
∴ BD = 2 × 60 = 120 metre
