$A+B+C=180^{\large\circ}$
$30^{\large\circ}+60^{\large\circ}+C=180^{\large\circ}$
$C=180^{\large\circ}-90^{\large\circ}$
$\;\;\;=90^{\large\circ}$
Now $\large\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
$a : b: c=\sin A :\sin B :\sin C$
$\qquad\quad\;\;=\sin 30^{\large\circ} :\sin 60^{\large\circ} :\sin 90^{\large\circ}$
$\qquad\quad\;\;=\large\frac{1}{2} :\frac{\sqrt 3}{2}$$ : 1$
$\qquad\quad\;\;=1:\sqrt 3 : 2$
Hence (c) is the correct answer.