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From the top of a tower 60 metre high the angle of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. If the pole and tower stand on the same plane, the height of the pole in metre is
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- 60 (√3 - 1)
- 20 (√3 - 1)
- 20 (3 - √3)
- 20 (√3 + 1)
Correct Option: C
AB = height of tower = 60 metre
BE = CD = height of pole
= h metre
BC = ED = x metre
In ∆ AED,
| tan 45° = | ED |
| ⇒ 1 = | x |
60 – h ... (i)
In ∆ ABC,
| tan 60° = | BC |
| ⇒√3 = | x |
⇒ √3 x = 60
| ⇒x = | = 20√3 metre | √3 |
From equation (i),
20 √3 = 60 – h
⇒ h = 60 - 20√3
= 20 (3 - √3) metre
