question_answer

A man observes the elevation of a balloon to be \[30{}^\circ \]. He then walks 1 km. towards the balloon and finds the angle of elevation now is \[60{}^\circ \]. The height (in km) of the balloon is

A)  \[\frac{\sqrt{3}}{2}\]                      

B)         \[\sqrt{3}+1\]

C)  \[\sqrt{3}-1\]   

D)         \[\frac{2}{\sqrt{3}}\]

Correct Answer: A

Solution :

 Let height of the balloon is h, and the man is first at A and after moving 1 km, he is at B. In            \[\Delta \,ABC,\angle ACB={{30}^{o}}\] and        \[\angle BAC={{30}^{o}}\] \[\therefore \]  s\[BC=AB=1\,km\] In   \[\Delta \,BOC,\]       \[h=BC\,\sin \,{{60}^{o}}=\frac{\sqrt{3}}{2}\]