https://file.aiquickdraw.com/mathbot/file/1727467899119c4fzqf3r.jpg

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°**.

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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.

It is exactly 7:20:47 in the morning. Determine the angle between the second hand and the minute hand.

Learn how to calculate the angle between the second hand and the minute hand at exactly 7:20:47. This problem covers clock angles, circular geometry, and involves converting seconds into fractional minutes. Suitable for students in Grades 9-10.

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