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)?

• A. \(\frac{{{\rm{r}}\sin {\rm{\beta }}}}{{\sin \left( {\frac{{\rm{\alpha }}}{2}} \right)}}\)
• B. \(\frac{{{\rm{r}}\sin {\rm{\beta }}}}{{\sin \left( {\frac{{\rm{\alpha }}}{4}} \right)}}\)
• C. \(\frac{{{\rm{r}}\sin \left( {\frac{{\rm{\beta }}}{2}} \right)}}{{\sin {\rm{\alpha }}}}\)
• D. \(\frac{{{\rm{r}}\sin {\rm{\alpha }}}}{{\sin \left( {\frac{{\rm{\beta }}}{2}} \right)}}\)