What is the angle between the two hands at 3 : 10 am?

Answer

To find the angle between the hour hand and the minute hand at 3:10 AM, we can use the formula:

\[ \text{Angle} = \frac{1}{2} \left| 60h - 11m \right| \]

where \( h \) is the hour and \( m \) is the minutes.

### Step-by-Step Solution:

1. **Identify the values of \( h \) and \( m \)**:
- Here, \( h = 3 \) (the hour) and \( m = 10 \) (the minutes).

2. **Substitute the values into the formula**:
\[ \text{Angle} = \frac{1}{2} \left| 60 \times 3 - 11 \times 10 \right| \]

3. **Calculate the expressions inside the absolute value**:
- Calculate \( 60 \times 3 = 180 \)
- Calculate \( 11 \times 10 = 110 \)
- Now substitute these values back into the equation:
\[ \text{Angle} = \frac{1}{2} \left| 180 - 110 \right| \]

4. **Subtract the values**:
\[ 180 - 110 = 70 \]

5. **Apply the absolute value**:
- Since \( 70 \) is already positive, we can drop the absolute value:
\[ \text{Angle} = \frac{1}{2} \times 70 \]

6. **Calculate the final angle**:
\[ \text{Angle} = 35 \text{ degrees} \]

### Final Answer:
The angle between the hour hand and the minute hand at 3:10 AM is **35 degrees**.