To solve this problem, we need to determine the angle between the second hand and the minute hand at exactly 7:20:47.

Step 1: Understanding the movement of the hands

1. Minute hand:

   • The minute hand completes a full circle (360°) in 60 minutes. Therefore, for each minute, it moves: $\frac{360°}{60} = 6° \text{ per minute}.$
   • Since the current time is 20 minutes and 47 seconds, we convert 47 seconds into a fraction of a minute: $\text{Total minutes} = 20 + \frac{47}{60} = 20.7833 \text{ minutes}.$
   • Therefore, the minute hand has moved: $\text{Angle of minute hand} = 20.7833 \times 6 = 124.7°.$

2. Second hand:

   • The second hand moves a full circle (360°) in 60 seconds. Therefore, for each second, it moves: $\frac{360°}{60} = 6° \text{ per second}.$
   • Since the current second is 47, the second hand is at: $\text{Angle of second hand} = 47 \times 6 = 282°.$

Step 2: Calculate the angle between the two hands

To find the angle between the second and minute hands, subtract the two angles and ensure the result is between 0° and 180° (since angles on a circle larger than 180° would be measured in the smaller direction).

$\text{Difference} = |282° - 124.7°| = 157.3°.$

Thus, the angle between the second hand and the minute hand at 7:20:47 is approximately 157.3°.

Would you like further details or clarifications? Here are 5 related questions for practice:

1. What would be the angle between the hour and minute hands at the same time?
2. How would the angle change if the time was 7:20:15 instead of 7:20:47?
3. Can you calculate the angle between the hour and second hands at 7:20:47?
4. What is the total movement of the second hand from 0 seconds to 47 seconds in degrees?
5. How long does it take for the minute hand to move 1 degree?

Tip: To find angles between clock hands, remember that the hands move in a predictable manner: the minute hand moves 6° per minute, and the second hand moves 6° per second.