Trigonometry! #59

Geometry Level 3

A round balloon of radius r 2 \frac {r}{2} subtends an angle α \alpha at the eye of the observer while the angle of elevation of its centre is 2 β 2\beta , then the height of the balloon is equal to which of the options?

This problem is part of the set Trigonometry .

r 2 csc ⁡ α 2 sin ⁡ β \frac {r}{2} \csc \frac {\alpha}{2} \sin \beta r sin ⁡ β 2 csc ⁡ α r \sin \frac {\beta}{2} \csc \alpha r 2 csc ⁡ α 2 sin ⁡ 2 β \frac {r}{2} \csc \frac {\alpha}{2} \sin 2\beta r sin ⁡ β csc ⁡ α 2 r \sin \beta \csc \frac {\alpha}{2}

Omkar Kulkarni by Omkar Kulkarni , 22, India

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