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A telegraph post is bent at a point above the ground due to storm. Its top just meets the ground at a distance of 8 √3 metres from its foot and makes an angle of 30°, then the height of the post is :
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- 16 metres
- 23 metres
- 24 metres
- 10 metres
Correct Option: C
AB = Telegraph post = h metre
Telegraph post bends at point D.
DB = x metre
∴ AD = CD = (h – x) metre
BC = 8 √3 metre
From, ∆ DBC,
| sin 30° = | DC |
| ⇒ | = | ⇒ 2x = h - x | ||
| 2 | h - x |
⇒ 3x = h ......... (i)
Again,
| tan 30° = | BC |
| ⇒ | = | |||
| √3 | 8√3 |
⇒ x = 8 metre
∴ h = 3 × 8 = 24 metre
