How many degrees is the smaller angle between the hands of the clock at 8:30 AM?
To determine the smaller angle between the hands of the clock at any given time, you need to know the positions of the hour and minute hands. Here's how you can calculate the smaller angle between the clock hands at 8:30 AM:
1. Understand the clock's hand positions: In a standard clock, the minute hand completes a full revolution (360 degrees) in 60 minutes, while the hour hand completes a full revolution in 12 hours. The hour hand moves gradually as the minutes progress.
2. Calculate the position of the hour hand: At 8:30 AM, the hour hand will be located between the 8 and 9 on the clock face since half an hour has passed. To determine its exact position, divide the number of minutes (30) by the number of minutes it takes for the hour hand to move from one hour mark to the next (60 minutes). Multiply this by the angle between each hour mark (30 degrees) to get the angle covered by the hour hand so far.
Angle covered by the hour hand = (30/60) * 30 degrees = 15 degrees
3. Calculate the position of the minute hand: At 8:30 AM, the minute hand will be pointing exactly at the 6 on the clock face since that denotes the 30-minute mark.
4. Find the angle between the hour and minute hands: To calculate the smaller angle between the hands, subtract the angle covered by the hour hand (15 degrees) from the angle covered by the minute hand (0 degrees).
Smaller angle between the hands = 0 degrees - 15 degrees = -15 degrees
Note: The negative angle indicates that the minute hand is counterclockwise to the hour hand. In this case, you can consider the smaller angle to be 360 degrees + (-15 degrees) = 345 degrees.
Therefore, the smaller angle between the hands of the clock at 8:30 AM is 345 degrees.