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On a ground, there is a vertical tower with a flagpole on its top. At a point 9 metre away from the foot of the tower, the angles of elevation of the top and bottom of the flagpole are 60° and 30° respectively. The height of the flagpole is :
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- 5 √3 metre
- 6 √3 metre
- 6 √2 metre
- 6 √5 metre
Correct Option: B
AB = Height of tower = h metre
AD = Height of flagstaff = x metre
∠BCD = 60°; ∠BCA = 30°
BC = 9 metre
In ∆ABC,
| tan 30° = | BC |
| ⇒ | = | √3 | 9 |
| ⇒ h = | = 3√3 metre | √3 |
In ∆BCD,
| tan 60° = | BC |
| ⇒ √3 = | 9 |
⇒ h + x = 9 √3
⇒ 3 √3 + x = 9 √3
⇒ x = 9 √3 – 3 √3
= 6 √3 metre
