Question

If $\theta$ is the measure of an acute angle and $\sqrt{3}\sin \theta =\cos \theta$ then $\theta =$ _________.

• A. ${90}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

$\theta$ is the measure of an acute angle
$\sqrt{3}\sin \theta =\cos \theta$
$\therefore \frac{\sin \theta }{\cos \theta }=\frac{1}{\sqrt{3}}$
$\therefore \tan \theta =\frac{1}{\sqrt{3}}$, but $\tan {30}^{\circ }=\frac{1}{\sqrt{3}}$
$\therefore \theta ={30}^{\circ }$.