To find the angle between the hour and minute hands at "quarter past 3" (3:15), execute the following steps:
1. Minute hand calculation: At 3:15, the minute hand is at the 15-minute mark. Each minute corresponds to 6 degrees (360°/60 minutes = 6°/minute). Therefore, its position is:
15 minutes × 6 degrees/minute = 90 degrees.
2. Hour hand calculation: The hour hand advances 30 degrees per hour (360°/12 hours = 30°/hour). At precisely 3:00, it is at 90 degrees (3 hours × 30°/hour). As 15 minutes represent 1/4 of an hour, the hour hand moves an additional distance:
(1/4) × 30 degrees = 7.5 degrees.
Consequently, at 3:15, the hour hand is located at:
90 degrees + 7.5 degrees = 97.5 degrees.
3. Angle determination: The angle between the hands is the absolute difference of their positions:
|97.5 degrees - 90 degrees| = 7.5 degrees.
The angle formed by the hour and minute hands at 3:15 is thus $7 \frac{1}{2}$ degrees.