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 \theta. If the aeroplane is at a height of 8 km above the ground, then which one of the following is correct?
- A. 0^\circ \lt \theta \lt 30^\circ
- B. 30^\circ \lt \theta \lt 45^\circ
- C. 45^\circ \lt \theta \lt 60^\circ ✓
- D. 60^\circ \lt \theta \lt 90^\circ
Correct Answer: C. 45^\circ \lt \theta \lt 60^\circ
Explanation
The distance from the observer to the plane (hypotenuse) is 10 km, and its height (perpendicular) is 8 km. Therefore, \sin \theta = \frac{8}{10} = 0.8. Since \sin 45^\circ \approx 0.707 and \sin 60^\circ \approx 0.866, the angle \theta must lie between 45^\circ and 60^\circ.
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