A) \[\frac{12\,\times \,3}{\sqrt{5}}\]
B) \[12\,\times \,3\,\times \,\sqrt{5}\]
C) \[\frac{12\,\times \,3}{\sqrt{7}}\]
D) \[12\,\times \,3\,\times \,\sqrt{7}\]
Correct Answer: C
Solution :
\[\tan \,{{i}_{c}}=\frac{r}{h}\] or \[r=h\,\tan {{i}_{c}}\] or \[r=h\frac{\sin \,{{i}_{c}}}{\cos \,{{i}_{c}}}\]or \[r=h\frac{\sin \,{{i}_{c}}}{\sqrt{1-{{\sin }^{2}}{{i}_{c}}}}\] But \[\sin \,{{i}_{c}}=\frac{1}{\mu }\] \[\therefore \] \[r=h\frac{\frac{1}{\mu }}{\sqrt{1-\frac{1}{{{\mu }^{2}}}}}\] \[=\frac{h}{\sqrt{{{\mu }^{2}}-1}}\] \[=\frac{12}{\sqrt{\frac{16}{9}-1}}=\frac{12\times 3}{\sqrt{7}}cm\]
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