A clock shows 3:15. What is the angle between the hour and the minute hand? (2023)

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Q: A clock shows 3:15. What is the angle between the hour and the minute hand? (2023)

Solution: At 3:15, the hour hand is at 97.5 degrees and the minute hand is at 90 degrees. The angle is 97.5 - 90 = 7.5 degrees.

Steps: 8

Step 1: Understand that a clock has two hands: the hour hand and the minute hand.
Step 2: Know that the clock is a circle, which is 360 degrees.
Step 3: Each hour on the clock represents 30 degrees (360 degrees / 12 hours = 30 degrees per hour).
Step 4: Calculate the position of the hour hand at 3:15. At 3:00, the hour hand is at 90 degrees (3 hours * 30 degrees).
Step 5: Since 15 minutes is a quarter of an hour, the hour hand moves an additional 7.5 degrees (30 degrees / 4 = 7.5 degrees).
Step 6: Add the additional movement to the hour hand's position: 90 degrees + 7.5 degrees = 97.5 degrees.
Step 7: Calculate the position of the minute hand at 15 minutes. The minute hand at 15 minutes is at 90 degrees (15 minutes * 6 degrees per minute, since 360 degrees / 60 minutes = 6 degrees per minute).
Step 8: Find the angle between the hour hand and the minute hand by subtracting their positions: 97.5 degrees - 90 degrees = 7.5 degrees.