question_answer

A round balloon of radius 'r' subtends an angle\[\alpha \]at the eye of an observer, while the angle of elevation of its centre is\[\beta \]. Find the height of the centre of the balloon.

A) \[r\sin \frac{\alpha }{2}\cos ec\beta \]

B)        \[r\cos ec\frac{\alpha }{2}\cos \beta \]

C) \[r\cos \frac{\alpha }{2}\cos ec\beta \]

D)        \[r\cos ec\frac{\alpha }{2}\sin \beta \]

Correct Answer: D

Solution :

In \[\therefore \]or\[=\left( \frac{144}{48}+\frac{384}{48}+\frac{240}{48} \right)=3+8+5=16\] In \[\frac{a}{b}\]or \[\frac{c}{d}=\frac{L.C.M.(a,c)}{H.C.F.(b,d)}\] \[\Rightarrow \]               \[L.C.M.\] \[\frac{6}{14}and\frac{2}{7}\] \[\Rightarrow \] \[\frac{L.C.M.(6,2)}{H.C.F.(14,7)}=\frac{6}{7}\] \[\text{7}\times \text{13}+\text{13}=\text{1}0\text{4}=\text{23}\times \text{13}\]