A) \[1:2\]
B) 2 :1
C) \[(\sqrt{5}+1):(\sqrt{5}-1)\]
D) \[(\sqrt{5}-1):(\sqrt{5}+1)\]
Correct Answer: C
Solution :
\[x+2x+7x={{180}^{o}}\Rightarrow x={{18}^{o}}\] Hence the angles are \[{{18}^{o}},\text{ }{{36}^{o}},\text{ }{{126}^{o}}\] Greatest side \[\propto \]\[\sin ({{126}^{o}})\] Smallest side \[\propto \] \[\sin ({{18}^{o}})\] and ratio\[=\frac{\sin {{126}^{o}}}{\sin ({{18}^{o}})}=\frac{\sqrt{5}+1}{\sqrt{5}-1}\].
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