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Two posts are 2 metres apart. Both posts are on same side of a tree. If the angles of depressions of these posts when observed from the top of the tree are 45° and 60° respectively, then the height of the tree is :
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- (3 - √3) metre
- (3 + √3) metre
- (- 3 + √3) metre
- (3 - √2) metre
Correct Option: B
CD = 2 metre
BD = x metre
AB = Tree = h metre
From ∆ ABC,
| tan 45° = | BC |
| ⇒ 1 = | x + 2 |
⇒ h = (x + 2) metre .....(i)
From ∆ ABD,
| tan 60° = | BD |
| ⇒ √3 = | x |
| ⇒ x = | ....(ii) | √3 |
From equations (i) and (ii),
| h = | + 2 | √3 |
| ⇒ h - | = 2 | √3 |
| ⇒ | h - h | = 2 | √3 |
⇒ h(√3 - 1) = 2 √3
| ⇒ h = | √3 - 1 |
| = | + 1) | (√3 - 1)(√3 + 1) |
| = | + 1) | = √3 (√3 + 1) | 3 - 1 |
= (3 + √3) metre
