Convert the following angle into radian: 65° 30'

To convert the angle \(65^\circ 30'\) into radians, follow these steps:

1. **Convert the angle in degrees and minutes to just degrees**:
- \( 30' \) represents 30 minutes.
- Since 1 degree = 60 minutes, we can convert minutes to a fraction of a degree:
\[
30' = \frac{30}{60} = 0.5^\circ
\]
- So, \( 65^\circ 30' = 65^\circ + 0.5^\circ = 65.5^\circ \).

2. **Convert degrees to radians**:
- The conversion formula from degrees to radians is:
\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\]
- Substitute \( 65.5^\circ \) into the formula:
\[
\text{radians} = 65.5 \times \frac{\pi}{180}
\]
- Simplify the expression:
\[
\text{radians} = \frac{65.5\pi}{180}
\]
- Now, compute the value:
\[
\text{radians} = \frac{65.5 \times 3.14159}{180}
\]
\[
\text{radians} \approx 1.142 \text{ radians}
\]

Thus, the angle \(65^\circ 30'\) is approximately equal to 1.142 radians.