2.1. (2 points) In a triangle, one of the angles is less than $50^{\circ}$, and another is less than $70^{\circ}$. Find the cosine of the third angle if its sine is $\frac{4}{7}$.
Answer: $-\frac{\sqrt{33}}{7} \approx-0.82$.

Solution. If $\sin \alpha=\frac{4}{7}$ and $\alpha>180^{\circ}-\left(50^{\circ}+70^{\circ}\right)=60^{\circ}$, then $|\cos \alpha|=\sqrt{1-\sin ^{2} \alpha}=\frac{\sqrt{33}}{7}$ and $\cos \alpha<\frac{1}{2}$, therefore $\cos \alpha=-\frac{\sqrt{33}}{7}$.