A clock shows 3:15. What is the angle between the hour and minute hands?

A clock shows 3:15. What is the angle between the hour and minute hands?

Step 1: Understand that the clock has two hands: the hour hand and the minute hand.
Step 2: Know that each hour on the clock represents 30 degrees (360 degrees / 12 hours = 30 degrees per hour).
Step 3: Calculate the position of the hour hand at 3:15. The hour hand is at 3 o'clock plus a little more because it's 15 minutes past 3.
Step 4: Calculate the degrees for the hour hand: 3 hours * 30 degrees/hour = 90 degrees.
Step 5: Since 15 minutes is a quarter of an hour, the hour hand moves an additional 0.5 degrees for each minute (30 degrees/hour / 60 minutes/hour = 0.5 degrees/minute).
Step 6: Calculate the additional movement of the hour hand for 15 minutes: 15 minutes * 0.5 degrees/minute = 7.5 degrees.
Step 7: Add the two parts together for the hour hand's total position: 90 degrees + 7.5 degrees = 97.5 degrees.
Step 8: Now calculate the position of the minute hand at 15 minutes. The minute hand at 15 minutes is at 90 degrees (15 minutes * 6 degrees/minute = 90 degrees).
Step 9: Find the angle between the hour hand and the minute hand by taking the absolute difference: |97.5 degrees - 90 degrees| = 7.5 degrees.

Clock Angles – Understanding how to calculate the angles between the hour and minute hands of a clock based on their positions.
Time Conversion – Converting time into degrees for both hour and minute hands using the formulas: hour hand = hours * 30 + minutes * 0.5 and minute hand = minutes * 6.