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The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electric pole and an angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
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- 5 m
- 8 m
- 10 m
- 12 m
- None of these
Correct Option: C
Let us draw the figure from the given question.
Let, AB be the tower and CD be the electric pole.
Let, BC = DE = x.
Given :- AB = 15 m
| Now In triangle ACB ; we have , | AB | = tan60° . | BC |
| ⇒ | 15 | = √3 | ⇒ | x = | 15 | . |
| x | √3 |
| Also ; In triangle ADE , | AE | = | tan30° |
| DE |
| ⇒ | = | ||
| 15/√3 | √3 |
⇒ 3y = 15 ⇒ y = 5
| ∴ | CD = BE = AB - AE | = | 15 - 5 = 10 m. |
Hence , the height of the electric pole is 10 m .
