SSC
Sample Paper
SSC-CGL TIER - I Sample Test Paper-6
question_answer
A spherical balloon of radius r subtends angle 60° at the eye of an observer. If the angle of elevation of its centre is 60° and h is the height of the centre of the balloon, then which one of the following is correct?
A)h = r
B)\[h=\sqrt{2}r\]
C)\[h=\sqrt{3}r\]
D)\[h=2r\]
Correct Answer:
C
Solution :
In \[\Delta ABO\], \[\sin {{60}^{{}^\circ }}\frac{OB}{AO}\Rightarrow AO=\frac{OB}{\sin {{60}^{{}^\circ }}}\] ? (i) Now, in\[\Delta AOC\], \[\Rightarrow \,\,\,\,\,\,\sin \left( \frac{{{60}^{{}^\circ }}}{2} \right)=\frac{OC}{AO}\] ? (ii) From Eqs. (i) and (ii), \[\frac{OB}{\sin {{60}^{{}^\circ }}}=\frac{OC}{\sin {{30}^{{}^\circ }}}\] \[\Rightarrow \,\,\,\,\,\frac{h}{\sqrt{3}}=\frac{r}{1}\Rightarrow \]