A) \[8\,a\,\sqrt{3}\]
B) \[4\,a\,\sqrt{3}\]
C) \[2\,a\,\sqrt{3}\]
D) \[a\,\sqrt{3}\]
Correct Answer: A
Solution :
In \[\Delta OCA,\,\,\,\tan {{30}^{o}}=\frac{AC}{OC}\] \[\Rightarrow \] \[\frac{1}{\sqrt{3}}=\frac{2at}{a{{t}^{2}}}\] \[\Rightarrow \] \[t=2\sqrt{3}\] Again in \[\Delta \,OCA,\] \[OA=\sqrt{O{{C}^{2}}+A{{C}^{2}}}\] \[=\sqrt{{{(a{{t}^{2}})}^{2}}+{{(2at)}^{2}}}\] \[=\sqrt{{{[{{(2\sqrt{3})}^{2}}]}^{2}}{{a}^{2}}+4{{a}^{2}}{{(2\sqrt{3})}^{2}}}\] \[=\sqrt{144\,{{a}^{2}}+48{{a}^{2}}}=\sqrt{192\,{{a}^{2}}}\] \[=8\sqrt{3}\,a\]You need to login to perform this action.
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