$$
\text { Let } A B C \text { be triangle and given that, }
$$


$$
\angle A: \angle B: \angle C=1: 2: 3
$$

Let the ratio be ' $x$ ', then
$$
\angle A=x, \angle B=2 x, \angle C=3 x
$$

Using angle sum property,
$$
\begin{aligned}
& \angle A+\angle B+\angle C=180^{\circ} \\
\Rightarrow & x+2 x+3 x=180 \Rightarrow x=30 \\
\therefore \quad & \angle A=30, \angle B=60, \angle C=90^{\circ}
\end{aligned}
$$


Using sine law of triangles,
$$
\begin{aligned}
& \quad \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\
\Rightarrow \quad \frac{\sin 30^{\circ}}{a} & =\frac{\sin 60^{\circ}}{b}=\frac{\sin 90^{\circ}}{c} \\
\Rightarrow \quad & \frac{1}{2 a}=\frac{\sqrt{3}}{2 b}=\frac{1}{c} \Rightarrow \frac{1}{a}=\frac{\sqrt{3}}{b}=\frac{2}{c} \\
\Rightarrow \quad & a: b: c=1: \sqrt{3}: 2
\end{aligned}
$$