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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance towards the tower and then his angle of elevation of the top of the tower is 60°. If the height of the tower is 30 m, then the distance he moves is
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- 22 m
- 22 √3 m
- 20 m
- 20 √3 m
Correct Option: D
AB = Tower = 30 metre
CD = x metre
∠ACB = 30°
∠ADB = 60°
From ∆ ABD
| tan60° = | BD |
| ⇒ √3 = | BD |
| ⇒ BD = | = 10√3 metre | √3 |
From ∆ ABC,
| tan30° = | BC |
| ⇒ | = | |||
| √3 | 10√3 + x |
⇒ 10 √3 + x = 30 √3
⇒ x = 30 √3 – 10 √3
= 20 √3 metre
