A) \[\frac{5\sqrt{3}}{2}\]
B) \[5\sqrt{\frac{3}{2}}\]
C) \[5\sqrt{\frac{2}{3}}\]
D) \[\frac{5\sqrt{2}}{3}\]
Correct Answer: B
Solution :
In \[\Delta OBC,\] we have \[\tan \alpha =\frac{5}{x}\] ?(i) \[\tan 2\alpha \,=\frac{30}{x}\] ?(ii) Dividing (ii) by (i) we have \[\tan 2\alpha \,=\frac{30}{5}\tan \alpha \] \[\Rightarrow \,\,\frac{2\tan \alpha }{1-{{\tan }^{2}}\alpha }\,=6\tan \alpha \Rightarrow \,{{\tan }^{2}}\alpha \,=\frac{2}{3}\] \[\Rightarrow \,\,\tan \alpha =\sqrt{\frac{2}{3}}\] \[\therefore \,\,x=5\,\cot \,\alpha \,=\sqrt{\frac{3}{2}}\]You need to login to perform this action.
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