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\[x,\text{ }x+1\]. In\[\Delta BCD,\] \[\tan 60{}^\circ =\frac{h}{x}\] \[\Rightarrow \] \[x=\frac{h}{\sqrt{3}}\] ??.(i) In\[\Delta ABC,\] \[\tan 30{}^\circ =\frac{h}{x+1}\] \[\Rightarrow \] \[\frac{1}{\sqrt{3}}=\frac{h}{x+1}\] \[\Rightarrow \] \[\frac{h}{\sqrt{3}}+1=\sqrt{3}h\] [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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