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The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar must be raised so that its angle of elevation at the same point may be 45°, is (Take, √3 = 1.732)
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- 63.4
- 86.6
- 126.8
- 173.2
Correct Option: A
AB = incomplete pole
BC = 150 metre
∠ACB = 30°
In ∆ABC,
| tan30° | BC |
| ⇒ | = | √3 | 150 |
| ⇒ AB = | = 50√3 metre | √3 |
In ∆BCD,
| tan45° = | BC |
| ⇒ 1 = | 150 |
⇒ BD = 150 metre
∴ AD = BD – AB
= (150 – 50 √3 ) metre
= 50 (3 - √3) metre
= 50 (3 – 1.732) metre
= (50 × 1.268) metre
= 63.4 metre
