A) \[3:5:2\]
B) \[1:\sqrt{3}:2\]
C) 3 : 2 : 1
D) 1: 2 : 3
Correct Answer: D
Solution :
We have \[a:b:c=1:\sqrt{3}:2\] i.e, \[a=\lambda ,\,b=\sqrt{3}\lambda ,\,c=2\lambda \] \[\cos A=\frac{3{{\lambda }^{2}}+4{{\lambda }^{2}}-{{\lambda }^{2}}}{2(\sqrt{3}\lambda )\,\,(2\lambda )}=\frac{6{{\lambda }^{2}}}{4\sqrt{3}{{\lambda }^{2}}}=\frac{\sqrt{3}}{2}\] \[\cos A=\frac{\sqrt{3}}{2}\] Þ \[A=30{}^\circ \] Similarly,\[\cos B=\frac{1}{2}\Rightarrow B=60{}^\circ \], \[\text{cos}\,C=0\Rightarrow C=90{}^\circ \]. Hence\[A:B:C=1:2:3\].
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