In the sides of a 30-degree angle, we drew triangles as shown in the figure. The points $A_{i}$ are on one side, and the points $B_{i}$ are on the other side: the angles $O A_{i} B_{i}$ are 120 degrees, and the angles $O B_{i} A_{i+1}$ are right angles. Determine the ratio of the areas of the triangles $A_{1} B_{1} A_{2}$ and $A_{48} B_{48} A_{49}$.

![](https://cdn.mathpix.com/cropped/2024_05_02_5df2143229b99329f40cg-1.jpg?height=415&width=702&top_left_y=302&top_left_x=690)