Description for Correct answer:
Given,

\( \Large \alpha + \beta =90 ^{\circ} \) and \( \Large \alpha : \beta =2:1 \)

\( \Large \alpha =\frac{2}{2+1} \times 90 ^{\circ} \)

= \( \Large \frac{2}{3} \times 90 ^{\circ} =60 ^{\circ} \)

Similarly, \( \Large \beta =\frac{1}{3} \times 90 ^{\circ} =30 ^{\circ} \)

\( \Large sin \alpha :sin \beta =sin60 ^{\circ} :sin30 ^{\circ} \)

= \( \Large \frac{\sqrt{3}}{2}:\frac{1}{2}=\sqrt{3}:1 \)