Task B-3.5. In a right-angled triangle, the ratio of the sines of the acute angles is $\sqrt{3}: 1$. Determine the angles of the triangle.
First solution.

$\frac{\sin \alpha}{\sin \beta}=\frac{\sqrt{3}}{1} \Rightarrow \frac{a}{b}=\frac{\sqrt{3}}{1} \Rightarrow a=\sqrt{3} b$

$\operatorname{tg} \alpha=\frac{a}{b}=\sqrt{3} \quad \Rightarrow \quad \alpha=60^{\circ}$

$\beta=90^{\circ}-60^{\circ}=30^{\circ}$