To calculate the angle between the hour and minute hands of a clock at 5:15, we need to determine the positions of each hand separately.
The minute hand moves 360 degrees in 60 minutes, which means for every minute, it moves 6 degrees. At 15 minutes, the minute hand will be:
Minute hand position: 15 minutes × 6 degrees/minute = 90 degrees
Now, for the hour hand, it moves 360 degrees in 12 hours, which means it moves 30 degrees for every hour. Additionally, it progresses further for each minute. Therefore, at 5:15, the hour hand’s position can be calculated as follows:
At 5 o’clock, the hour hand is at:
Hour hand position at 5:00: 5 hours × 30 degrees/hour = 150 degrees
For the additional 15 minutes, the hour hand moves further:
15 minutes means an additional:
15 minutes × 0.5 degrees/minute (since the hour hand moves 30 degrees in 60 minutes) = 7.5 degrees
Thus, the total position of the hour hand at 5:15 is:
150 degrees + 7.5 degrees = 157.5 degrees
Now, we find the angle between the two hands:
Angle between hands: |157.5 degrees – 90 degrees| = 67.5 degrees
Therefore, the angle between the hands of the clock at 5:15 is 67.5 degrees.