A) \[\pi /6\]
B) \[\pi /4\]
C) \[5\pi /12\]
D) \[\pi /2\]
Correct Answer: C
Solution :
\[2B=A+C\]and \[A+B+C=\pi \,\Rightarrow \,B=60{}^\circ \] Also \[\frac{\sin \,B}{\sin \,C}=\frac{\sqrt{3}}{\sqrt{2}}\,=\frac{\sqrt{3}}{2}.\frac{1}{\sin \,C}\] \[\sin \,C=\frac{1}{\sqrt{2}}\Rightarrow C=45{}^\circ \,\Rightarrow \,A=75{}^\circ \]
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