In ∆ABC, if $\angle$A = $30^\circ$, $\angle$B = $60^\circ$, then the ratio of sides is ______.

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In ∆ABC, if $\angle$A = $30^\circ$, $\angle$B = $60^\circ$, then the ratio of sides is bbunderline(1 : sqrt(3) : 2). Explanation: Let us assume the length of the side opposite to $\angle$B = x. In ΔABC, we have sin($\angle$B) = sin $30^\circ$ = x/(AB) $\Rightarrow$ $\frac{1}{2}$ = x/(AB) $\Rightarrow$ AB = 2x ...(i) And, tan $30^\circ$ = x/(BC) $\Rightarrow$ 1/sqrt3 = x/(BC) $\Rightarrow$ BC = sqrt3x ...(ii) $\therefore$ AC : BC : AB = x : x$\sqrt$3 : 2x = 1 : $\sqrt$3 : 2

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