A) \[{{30}^{o}}\]
B) \[{{15}^{o}}\]
C) \[{{75}^{o}}\]
D) \[{{45}^{o}}\]
Correct Answer: C
Solution :
Since A, B, C are in AP. \[\therefore \] \[B=\frac{A+C}{2}\] \[\Rightarrow \] \[B={{90}^{o}}-\frac{B}{2}\] \[(\therefore \,A+B+C={{180}^{o}})\] \[\Rightarrow \] \[B={{60}^{o}}\] Using sine rule, \[\frac{\sin \,B}{b}=\frac{\sin C}{c}\] \[\therefore \] \[\frac{\sin {{60}^{o}}}{\sqrt{3}}=\frac{\sin \,C}{\sqrt{2}}\] \[\Rightarrow \] \[\frac{\sqrt{3}}{2\sqrt{3}}=\frac{\sin C}{\sqrt{2}}\] \[\Rightarrow \] \[\sin C=\frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[C={{45}^{o}}\] \[\therefore \] \[A={{180}^{o}}-({{60}^{o}}+{{45}^{o}})\] \[={{75}^{o}}\]
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