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From the top of a tower of height 180 m the angles of depression of two objects on either sides of the tower are 30° and 45°. Then the distance between the objects are
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- 180 (3 + √3) m
- 180 (3 - √3) m
- 180 (√3 - 1) m
- 180 (√3 + 1) m
Correct Option: D
AD is tower and B and C are two objects,
∠ABD = 30° and ∠ACD = 45°
AD = 180 metre
From ∆ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | BD |
⇒ BD = 180 √3 metre
From ∆ADC,
| tan 45° = | DC |
| ⇒ 1 = | ⇒ DC = 180 metre | DC |
∴ BC = BD + DC
= 180 √3 + 180
= 180 ( √3 + 1) metre
