A spherical balloon of radius r subtends an angle alpha at the eye of an observer while the angle of...........

Mathematics (NDA) Coordinate Geometry

A spherical balloon of radius r subtends an angle α at the eye of an observer, while the angle of elevation of its centre is β.What is the height of the centre of the balloon (neglecting the height of the observer)?

$\frac{rsin\beta }{sin(\frac{\alpha }{2})}$

$\frac{rsin\beta }{sin(\frac{\alpha }{4})}$

$\frac{rsin\frac{\beta}{2} }{sin\alpha}$

$\frac{rsin\alpha }{sin\frac{\beta }{2}}$

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Explanation:

Let H be the height and R be the distance of centre of balloon from the observer.
$R=\frac{r}{sin\frac{\alpha }{2}}$
$H=Rsin\beta =\frac{rsin\beta }{sin\frac{\alpha }{2}}$