To find how the angle of $21.641^\circ$ was obtained from the calculation, we need to convert the radian value $0.3777 \, \text{rad}$ into degrees.

The formula to convert radians to degrees is:

$\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}$

Applying this conversion to $0.3777 \, \text{rad}$:

$\text{Degrees} = 0.3777 \times \frac{180}{\pi} \approx 21.641^\circ$

This is how the value $21.641^\circ$ was derived. It represents the phase angle in degrees.

Would you like further details on any other part of this calculation?

Here are some related questions:

1. How is the radian value derived for different distances?
2. Can we calculate the impedance $Z_c$ for other $L$ and $C$ values?
3. What impact does frequency $f$ have on the value of $\beta$?
4. Why is the angle conversion important in transmission line calculations?
5. How does the length $l$ affect the total phase shift?

Tip: Always keep track of units when calculating phase angles, as mixing radians and degrees can lead to significant errors.