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In any triangle, if the angles are in the ratio $1: 2: 3$, then their corresponding sides are in the ratio.
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Verified Answer
The correct answer is:
$1: \sqrt{3}: 2$
Ratio of angle of triangles are $1: 2: 3$.
$\therefore$ Angles of triangles are $30^{\circ}, 60^{\circ}$ and $90^{\circ}$.
Ratio of sides of triangle are
$$
\begin{array}{r}
\sin 30^{\circ} \cdot \sin 60^{\circ} \cdot \sin 90^{\circ} \\
\Rightarrow \quad \frac{1}{2}: \frac{\sqrt{3}}{2}=1 \Rightarrow 1: \sqrt{3}: 2
\end{array}
$$
$\therefore$ Angles of triangles are $30^{\circ}, 60^{\circ}$ and $90^{\circ}$.
Ratio of sides of triangle are
$$
\begin{array}{r}
\sin 30^{\circ} \cdot \sin 60^{\circ} \cdot \sin 90^{\circ} \\
\Rightarrow \quad \frac{1}{2}: \frac{\sqrt{3}}{2}=1 \Rightarrow 1: \sqrt{3}: 2
\end{array}
$$
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