If a clock shows 3:15, what is the angle between the hour and the minute hand?
Practice Questions
1 question
Q1
If a clock shows 3:15, what is the angle between the hour and the minute hand?
7.5 degrees
22.5 degrees
45 degrees
52.5 degrees
At 3:15, the hour hand is at 97.5 degrees (3 hours * 30 + 15 minutes * 0.5) and the minute hand is at 90 degrees (15 minutes * 6). The angle between them is |97.5 - 90| = 7.5 degrees.
Questions & Step-by-step Solutions
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Q
Q: If a clock shows 3:15, what is the angle between the hour and the minute hand?
Solution: At 3:15, the hour hand is at 97.5 degrees (3 hours * 30 + 15 minutes * 0.5) and the minute hand is at 90 degrees (15 minutes * 6). The angle between them is |97.5 - 90| = 7.5 degrees.
Steps: 10
Step 1: Understand that a 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).
Step 3: Calculate the position of the hour hand at 3:15. The hour hand is at 3 hours, which is 3 * 30 = 90 degrees.
Step 4: Since it's 15 minutes past 3, the hour hand moves further. Each minute, the hour hand moves 0.5 degrees (30 degrees / 60 minutes).
Step 5: Calculate the additional movement of the hour hand for 15 minutes: 15 minutes * 0.5 degrees = 7.5 degrees.
Step 6: Add the two positions of the hour hand together: 90 degrees + 7.5 degrees = 97.5 degrees.
Step 7: Now calculate the position of the minute hand. Each minute represents 6 degrees (360 degrees / 60 minutes).
Step 8: For 15 minutes, the minute hand is at 15 * 6 = 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|.
