What is the angle between hour-hand and minute-hand as 2 : 25 pm?

Options

A. `77.5^(@)`
B. `68^(@)`
C. `67.5^(@)`
D. none of these

Answer

To find the angle between the hour hand and the minute hand at 2:25 PM, 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 \( m \)**:
- At 2:25 PM, \( h = 2 \) (the hour) and \( m = 25 \) (the minutes).

2. **Substitute the values into the formula**:
\[ \text{Angle} = \frac{1}{2} \left| 60 \times 2 - 11 \times 25 \right| \]

3. **Calculate \( 60h \)**:
\[ 60 \times 2 = 120 \]

4. **Calculate \( 11m \)**:
\[ 11 \times 25 = 275 \]

5. **Substitute these values back into the formula**:
\[ \text{Angle} = \frac{1}{2} \left| 120 - 275 \right| \]

6. **Calculate the difference**:
\[ 120 - 275 = -155 \]

7. **Take the absolute value**:
\[ \left| -155 \right| = 155 \]

8. **Complete the calculation**:
\[ \text{Angle} = \frac{1}{2} \times 155 = 77.5 \]

9. **Final Result**:
The angle between the hour hand and the minute hand at 2:25 PM is \( 77.5^\circ \).