2. Compare two numbers: $\sqrt{3} \sin 10^{\circ}$ and $\sin 80^{\circ}$.
Answer: the second is greater

Solution: Consider the difference between the first and second numbers:

$$
\begin{aligned}
& \sqrt{3} \sin 10^{\circ}-\sin 80^{\circ}=\sqrt{3} \sin 10^{\circ}-\cos 10^{\circ}=2\left(\frac{\sqrt{3}}{2} \sin 10^{\circ}-\frac{1}{2} \cos 10^{\circ}\right)= \\
& =2\left(\cos 30^{\circ} \sin 10^{\circ}-\sin 30^{\circ} \cos 10^{\circ}\right)=2 \sin \left(10^{\circ}-30^{\circ}\right)=-\sin 20^{\circ}<0
\end{aligned}
$$

Grading criteria: Correct and justified solution - 7 points, incorrect solution or only answer - 0 points.