Q66 / 160 · TS EAMCET 2018 (05 May Shift 2) · Mathematics

In any triangle, if the angles are in the ratio $1: 2: 3$, then their corresponding sides are in the ratio.

  • A
    $1: \sqrt{2}: 1$
  • Correct answer
    B
    $1: \sqrt{3}: 2$
  • C
    $1: \sqrt{3}: 1$
  • D
    $1: 1: \sqrt{2}$

Solution

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 $$ \begin{array}{r} \sin 30^{\circ} \cdot \sin 60^{\circ} \cdot \sin 90^{\circ} \\ \Rightarrow \quad \frac{1}{2}: \frac{\sqrt{3}}{2}=1 \Rightarrow 1: \sqrt{3}: 2 \end{array} $$

Hence, the correct answer is option: 'B'.

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