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From an aeroplane just over a straight road, the angles of depression of two consecutive kilometre stones situated at opposite sides of the aeroplane were found to be 60° and 30° respectively. The height (in km) of the aeroplane from the road at that instant, is
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√3 2 -
√3 3 -
√3 4 - √3
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Correct Option: C
A = Position of aeroplane
B and C are km stones,
∠ABD = 60°, ∠ACD = 30°
BD = x km.
∴ CD = (1 – x) km.
In ∆ABD,
| tan 60° = | BD |
| ⇒ √3 = | x |
⇒ AD = √3 x km. ...(i)
In ∆ACD,
| tan 30° = | CD |
| ⇒ | = | √3 | 1 - x |
| ⇒ AD = | km. ...(ii) | √3 |
∴ From equations (i) and (ii),
| √3 x = | √3 |
⇒ 3x = 1 – x
| &rArrr; 4x = 1 ⇒ x = | km. | 4 |
| ∴ AD = √3 x = | km. | 4 |
