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The angle of elevation of an aeroplane as observed from a point 30 metre above the transparent water-surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water-surface of the lake is
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- 60 metre
- 45 metre
- 50 metre
- 75 metre
Correct Option: A
AB = transparent water-surface ∆CPM = 30°; ∠C’PM = 60°
CM = h
CB = h + 30
∴ C’B = h + 30
In ∆CMP,
| tan 30° = | |
| PM |
| ⇒ | ⇒ | ||
| √3 | PM |
⇒ PM = 3h ..... (i)
In ∆PMC’
| tan 60° = | |
| PM |
| ⇒ √3 = | |
| PM |
| ⇒ PM = | ...(ii) | |
| √3 |
| ∴ √3h = | ||
| √3 |
⇒ 3h = h + 60
⇒ 2h = 60
⇒ h = 30
∴ CB = BM + CM = 30 + 30 = 60 metre
