In a triangle, if the angles are in the ratio $3: 2: 1$, then the ratio of its sides is

In a triangle, if the angles are in the ratio $3: 2: 1$, then the ratio of its sides is
  1. $1: 2: 3$
  2. $2: \sqrt{3}: 1$
  3. $3: \sqrt{2}: 1$
  4. $1: \sqrt{3}: 3$

Solution

Let the angles be $3 x, 2 x, x$ $\begin{aligned} & 6 x=180^{\circ} \Rightarrow x=30^{\circ} ; \text { Angles are } 90^{\circ}, 60^{\circ}, 30^{\circ} \\ & a: b: c=\sin \mathrm{A}: \sin \mathrm{B}: \sin \mathrm{C} \\ & =1: \frac{\sqrt{3}}{2}: \frac{1}{2}=2: \sqrt{3}: 1 \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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