b) \( \hat{a}=21^{\circ} 49^{\prime 16^{\prime \prime}} \)

It looks like you are providing an angle in degrees, minutes, and seconds format. The angle \( \hat{a} = 21^{\circ} 49^{\prime} 16^{\prime\prime} \) can be interpreted as follows: - \( 21^{\circ} \) represents the degrees. - \( 49^{\prime} \) represents the minutes (where 1 minute = \( \frac{1}{60} \) of a degree). - \( 16^{\prime\prime} \) represents the seconds (where 1 second = \( \frac{1}{3600} \) of a degree). To convert this angle into decimal degrees, you can use the following formula: \[ \text{Decimal Degrees} = \text{Degrees} + \left(\frac{\text{Minutes}}{60}\right) + \left(\frac{\text{Seconds}}{3600}\right) \] Substituting the values: \[ \text{Decimal Degrees} = 21 + \left(\frac{49}{60}\right) + \left(\frac{16}{3600}\right) \] Calculating each part: 1. \( \frac{49}{60} \approx 0.81667 \) 2. \( \frac{16}{3600} \approx 0.00444 \) Now, adding these together: \[ \text{Decimal Degrees} \approx 21 + 0.81667 + 0.00444 \approx 21.82111 \] Thus, the angle \( \hat{a} \) in decimal degrees is approximately \( 21.82111^{\circ} \).