2022 · Q53
An aeroplane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation on the ground and makes an angle of elevation θ. If the aeroplane is at a height of 8 km above the ground, then which one of the following is correct?
Elementary MathematicsTrigonometry
- A0
- B30
- C45
- D60
Explanation
The 10 km is the line-of-sight distance (hypotenuse), so sinθ = 8/10 = 0.8. Since sin45° ≈ 0.707 < 0.8 < sin60° ≈ 0.866, we get 45° < θ < 60° (θ ≈ 53.1°). The printed options were these ranges; the source transcription shows only the lower bounds. Key disputed: a widely circulated third-party Set-A key lists B, but the hypotenuse reading (confirmed by published solutions) gives θ in (45°,60°). Hence the keyed option is C.