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The angles of elevation of top and bottom of a flag kept on a flagpost from 30 metres distance, are 45° and 30° respectively. Height of the flat is [taking √3 = 1.732]
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- 12 √3 metre
- 15 metre
- 14.32 metre
- 12.68 metre
Correct Option: D
AD = flag = x metre
AB = flagpost = h metre
BC = 30 metre
∠ACB = 45°; ∠DCB = 30°
From ∆ ABC,
| tan 45° = | BC |
| ⇒ 1 = | ⇒ h = 30 metre | 30 |
From ∆ BCD,
| tan 30° = | ⇒ | = | BC | √3 | 30 |
| ⇒ | = | = 90 | √3 | 30 |
| ⇒ 30 - x = | = 10√3 | √3 |
⇒ x = 30 – 10 √3
= 30 – 10 × 1.732
= 30 – 17.32
= 12.68 metre
