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The angle of elevation of the top of a TV tower from three points A, B, C in a straight line through the foot of the tower are α, 2α, 3α, respectively. If AB = a, the height of the tower is :
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- a tan α
- a sin α
- a sin 2α
- a sin 3α
Correct Option: C
Let us draw the figure from the given question.
Let, OP be a vertical tower. The elevation of top P from A, B, C are α, 2α, 3α, respectively. ∠APB = 2α - α= ∠PAB.
Given :- AB = a
In triangle OBP ,
| ∴ | OP | = | sin 2α | BP |
| ∴ | OP = | BP sin 2α | = a sin 2α. |
| Thus, height of the tower | = | a sin 2α. |
