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A pole being broken by the wind, the top struck the ground at an angle of 30° and at a distance of 21 m from the foot of the pole. Find out the total height of the pole.
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- 21 m
- 21 √3 m
- 21/ √3
- None of these
Correct Option: B
Let us draw the figure from the given question.
Let, OAP be the pole. When broken by wind at A .
let its top P strike the ground at P' so that OP' = 21 m, ∠OP'A = 30°, AP = AP'.
| We have, tan 30° = | OA | ⇒ | OA | = | 21 |
| OP' | √3 |
 ∴ tan30° = | 1 |  |
| √3 |
| Also, | AP' | = | sec 30° ⇒ | AP | = | 2 | [ ∴ AP = AP' ] |
| OP' | 21 | √3 |
| ∴ AP | = | 42 | = | 14√3 | ⇒ AP = | 14√3. |
| √3 |
Height of the pole = OP = OA + AP = 7√3 + 14√3 = 21√3.
