2021 · Q51
From an aeroplane flying above a river at an altitude of 1200 m, it is observed that the angles of depression of opposite points on the two banks of a river are 30° and θ. If the width of the river is 3000 m, then which one of the following is correct ?
Elementary MathematicsTrigonometry
- Aθ < 30°
- B30° < θ < 45°
- C45° < θ < 60°
- D60° < θ < 90°
Explanation
Let the near bank be at horizontal distance w₁: tan 30° = 1200/w₁ gives w₁ = 1200√3 ≈ 2078 m. The far bank is then w₂ = 3000 − 2078 = 922 m away, so tan θ = 1200/922 ≈ 1.30. Hence θ ≈ 52.5°, which lies between 45° and 60°, option (c).