A balloon of radius r subtends an angle $\alpha$ at the eye of an observer and the elevation of the centre of
the balloon from the eye is  $\beta$, the height $h$ of the centre of
the balloon is given by 

Let$O$ be the centre of the balloon of radius
$r$which subtends an angle $\alpha$ at $E,$ the eye of the observer.

If $EA$ and $EB$ are the tangents to the balloon, then $\angle OEA$

$=\angle OEA$ $=\alpha /2\left(\text{ Fig. 27.32 }\right)$

Let $OL = h$ be the height of the centre of the balloon,
then from  $\mathrm{\Delta }OLE$

$\begin{array}{l}h=OE\sin \beta \\ =r\mathrm{cosec}(\alpha /2)\sin \beta \\ =r\sin \beta /\sin (\alpha /2)\end{array}$