Trigonometryhard · Past Paper
A round balloon of radius r subtends an angle θ at the eye of an observer, while the angle of elevation of its center is φ. Height of center?
Ar sinφ cosec(θ/2)
Br sinφ sin(θ/2)
Cr cosφ cosec(θ/2)
Dr sin(θ/2) cosecφ
✓ Correct Answer: A — r sinφ cosec(θ/2)
Distance to center d: r/d = sin(θ/2) => d = r cosec(θ/2). Height H: H/d = sin φ => H = r cosec(θ/2) sin φ.
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