A) b
B) 2b
C) \[\sqrt{2b}\]
D) \[\sqrt{3}b\]
Correct Answer: B
Solution :
\[A={{45}^{o}},C={{60}^{o}},A+B+C=\pi \Rightarrow B={{75}^{o}}\] Þ \[a+c\sqrt{2}=k\sin A+k\sin C(\sqrt{2})\] \[=k\sin {{45}^{o}}+\sqrt{2}k\sin {{60}^{o}}\] \[=2k\left( \frac{\sqrt{3}+1}{2\sqrt{2}} \right)=2k\sin {{75}^{o}}=2k\sin B\] \ \[a+c\sqrt{2}=2b\].
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