To calculate the angle between the hour and minute hands of a clock at 3 PM, we can follow a straightforward formula. The clock is divided into 12 hours, with each hour marking a 30-degree segment on the clock face (360 degrees divided by 12 hours equals 30 degrees per hour).
1. **Position of the Hour Hand:** At 3 PM, the hour hand points directly at the 3. Since each hour represents 30 degrees, we can calculate the angle of the hour hand from the 12 o’clock position as follows:
- Hour hand angle = Hour × 30 = 3 × 30 = 90 degrees
2. **Position of the Minute Hand:** At 3 PM, the minute hand points to the 12. The angle for the minute hand at the top of the hour (i.e., 0 minutes) is:
- Minute hand angle = 0 minutes × 6 = 0 degrees
3. **Calculating the Angle Between the Two Hands:** Now that we have the angles for both hands, we subtract the smaller angle from the larger angle to find the angle between them:
- Angle between the hour and minute hands = |Hour hand angle – Minute hand angle|
- Angle = |90 degrees – 0 degrees| = 90 degrees
Thus, at 3 PM, the angle between the hour and minute hands of the clock is 90 degrees. This angle represents a right angle, which is quite characteristic of this time on the clock.