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From a tower 125 metres high, the angle of depression of two objects, which are in horizontal line through the base of the tower, are 45° and 30° and they are on the same side of the tower. The distance (in metres) between the objects is
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- 125 √3
- 125( √3 – 1)
- 125/( √3 – 1)
- 125( √3 + 1)
Correct Option: B
AB = Tower = 125 metre
BC = x metre, BD = y metre
From ∆ABC,
| tan 45° = | BD |
| ⇒ 1 = | ⇒ x = 125 metre | x |
From ∆ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | y |
⇒ y = 125 √3 metre
⇒ CD = y – x = 125 √3 – 125
= 125 ( √3 – 1) metre
