A) \[\frac{4}{\sqrt{3}}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{2}{\sqrt{3}}\]
D) 2
Correct Answer: B
Solution :
Let the distance of two consecutive stones are x, \[x+1\]. In \[\Delta BCD,\] \[\tan \,{{60}^{o}}=\frac{h}{x}\] \[\Rightarrow \] \[x=\frac{h}{\sqrt{3}}\] ??.(i) In \[\Delta ABC,\] \[\tan {{30}^{o}}=\frac{h}{x+1}\] \[\Rightarrow \] \[\frac{1}{\sqrt{3}}=\frac{h}{x+1}\] \[\Rightarrow \] \[\frac{h}{\sqrt{3}}+1=\sqrt{3}\,h\] (From (i)) \[\Rightarrow \] \[\frac{2h}{\sqrt{3}}=1\] \[\Rightarrow \] \[h=\frac{\sqrt{3}}{2}km\]You need to login to perform this action.
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