A) \[\frac{7}{13}\]
B) \[\frac{4}{3}\]
C) \[13\]
D) \[\frac{13}{7}\]
E) \[4\]
Correct Answer: C
Solution :
\[{{\sin }^{-1}}\left( \frac{5}{x} \right)+{{\sin }^{-1}}\left( \frac{12}{x} \right)=\frac{\pi }{2}\] \[\Rightarrow \]\[{{\sin }^{-1}}\left( \frac{5}{x} \right)+{{\cos }^{-1}}\sqrt{1-{{\left( \frac{12}{x} \right)}^{2}}}=\frac{\pi }{2}\] This is possible only when \[{{\left( \frac{5}{x} \right)}^{2}}=1-{{\left( \frac{12}{x} \right)}^{2}}\] \[\Rightarrow \] \[\frac{25+144}{{{x}^{2}}}=1\] \[\Rightarrow \] \[{{x}^{2}}=169\] \[\Rightarrow \] \[x=13\]
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