If the arcs of same length in two circles subtend angles of `60^(@)` and `75^(@)` at their centers. Find the ratio of their radaii.

Explanation

To solve the problem of finding the ratio of the radii of two circles that subtend angles of \(60^\circ\) and \(75^\circ\) at their centers for the same arc length, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Information:**
- Let the angle subtended by the arc in the first circle be \(\theta_1 = 60^\circ\).
- Let the angle subtended by the arc in the second circle be \(\theta_2 = 75^\circ\).
- Let the radius of the first circle be \(R_1\).
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