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From the top of a 20 metre high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is at 45°, then the height of the tower is (√3 = 1.732)
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- 45.46 metre
- 45.64 metre
- 54.64 metre
- 54.46 metre
Correct Option: C
AB = Height of building = 20 metre
CD = Height of tower = h metre (let)
∠ACB = ∠EAC = 45°
∠DAE = 60°
BC = AE = x metre
In ∆ABC,
| tan 45° = | ||
| BC |
| ⇒ 1 = | ||
| x |
⇒ x = 20 metre
In ∆ADE,
| tan 60° = | ⇒ √3 = | ||
| AE | 20 |
&RArr; h – 20 = 20√3
⇒ h = 20√3 + 20
= 20(√3 + 1)metre
= 20 (1.732 + 1) metre
= (20 × 2.732) metre
= 54.64 metre
