Question

In the given figure, a circle is given with centre O. The measure of the angle AOB is:

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

Answer 1

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

We have the $(x,y)$ coordinates as $A(\sqrt{3},1)$.
We know that the $x$ & $y$ coordinates are the perpendicular distance of the point from the $y$ and $x$ axis respectively.
Therefore, we can say that $\tan \theta =$ $\frac{1}{\sqrt{3}}$, where $\theta =\angle AOB$.
The angle given is an acute angle,
$\Rightarrow$The angle is ${30}^{\circ }$.