A) \[\sqrt{2}:2:(\sqrt{3}+1)\]
B) \[2:\sqrt{2}:(\sqrt{3}+1)\]
C) \[\sqrt{2}:(\sqrt{3}+1):2\]
D) \[2:(\sqrt{3}+1):\sqrt{2}\]
Correct Answer: A
Solution :
Obviously, the angles are\[{{30}^{o}},{{45}^{o}},{{105}^{o}}\]. \[\therefore \] \[a:b:c=\sin {{30}^{o}}:\sin {{45}^{o}}:\sin {{105}^{o}}\] \[=\frac{1}{2}:\frac{1}{\sqrt{2}}:\frac{\sqrt{3}+1}{2\sqrt{2}}=\sqrt{2}:2:(\sqrt{3}+1)\].
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