If the arcs of same length in two circles subtend angles of `30^(@)` and `45^(@)` at their centers, then find the ratio of their radii.

Explanation

To solve the problem, we need to find the ratio of the radii of two circles given that the arcs of the same length subtend angles of \(30^\circ\) and \(45^\circ\) at their centers.

### Step-by-Step Solution:

1. **Understanding the Arc Length Formula**:
The formula for the arc length \(l\) of a circle is given by:
\[
l = r \cdot \theta
...