Question

If $\sqrt{2}$ sin$({60}^{\circ }-\alpha )=1,$ then $\alpha$ is:

• A. ${45}^{\circ }$
• B. ${15}^{\circ }$
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is B ${15}^{\circ }$

$\sqrt{2}\sin (60°-\alpha )=1$

$\Rightarrow \sin (60°-\alpha )=\frac{1}{\sqrt{2}}$

$\Rightarrow \sin (60°-\alpha )=\sin 45°$

$\Rightarrow (60°-\alpha )=45°$

$\Rightarrow \alpha =15°$

Hence, the answer is $15°.$