\(T \alpha \frac{1}{\sqrt{ B \cos \theta}} \Rightarrow \frac{T_1}{ T _2}=\sqrt{\frac{ B _2 \cos \theta_2}{ B _1 \cos \theta_1}}\)

\(\Rightarrow \frac{60 / 20}{60 / 30}=\sqrt{\frac{ B _2}{ B _1} \frac{\cos 60^{\circ}}{\cos 30^{\circ}}} \Rightarrow \frac{3}{2}=\sqrt{\frac{ B _2}{\sqrt{33} B _1}}\)

\(\Rightarrow \frac{9}{4}=\frac{ B _2}{\sqrt{3} B _1} \Rightarrow \frac{ B _1}{ B _2}=\frac{4}{9 \sqrt{3}}=\frac{4}{\sqrt{243}}\)