Step 1: Understanding the position of the hour and minute hands.
At 02:15:
The minute hand is at the 3 o'clock position (15 minutes), which corresponds to 90° from the 12 o'clock position.
The hour hand is at a position between 2 and 3. To find its position at 02:15, we calculate how much it has moved from 2:00.
Step 2: Calculate the angle of the hour hand.
At 2:00, the hour hand is at the 2 position, which is: {Angle at 2:00} = (360 / 12) × 2 = 60°
Since the hour hand moves 30° every hour, in 15 minutes (which is a quarter of an hour), the hour hand will have moved: (30 / 60) × 15 = 7.5°
So, at 2:15, the hour hand is at: 60° + 7.5° = 67.5°
Step 3: Calculate the angle between the hour and minute hands.
Now, we can calculate the angle between the hour and minute hands: {Angle between hour and minute hands} = |90° - 67.5°| = 22.5°
Step 4: Conclusion.
Thus, the acute angle between the hour and minute hands at 02:15 is 22.5°, and the correct answer is (3) 22.5°.