Question

If $x+y={90}^o$ and $\sin x:\sin y=\sqrt{3}:1$, then what is $x:y$ equal to?

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $3:2$

Answer 1

The correct option is C $2:1$

$x+y={90}^{\circ }\Rightarrow siny=sin({90}^{\circ }-x)=cosx$

$\Rightarrow \frac{sinx}{cosx}=\sqrt{3}\Rightarrow tanx=\sqrt{3}\Rightarrow x={60}^{\circ },y={30}^{\circ }$

$\therefore x:y=2:1$