If a clock shows 12:45, what is the angle between the hour and minute hands?
Practice Questions
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Q1
If a clock shows 12:45, what is the angle between the hour and minute hands?
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At 12:45, the hour hand is at 337.5 degrees (12 * 30 + 45 * 0.5) and the minute hand is at 270 degrees (45 * 6). The angle between them is |337.5 - 270| = 67.5 degrees.
Questions & Step-by-step Solutions
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Q
Q: If a clock shows 12:45, what is the angle between the hour and minute hands?
Solution: At 12:45, the hour hand is at 337.5 degrees (12 * 30 + 45 * 0.5) and the minute hand is at 270 degrees (45 * 6). The angle between them is |337.5 - 270| = 67.5 degrees.
Steps: 4
Step 1: Understand that a clock has 12 hours and each hour represents 30 degrees (360 degrees / 12 hours).
Step 2: Calculate the position of the minute hand. Since there are 60 minutes in an hour, each minute represents 6 degrees (360 degrees / 60 minutes). At 45 minutes, the minute hand is at 45 * 6 = 270 degrees.
Step 3: Calculate the position of the hour hand. Each hour is 30 degrees, so at 12:00, the hour hand is at 0 degrees. At 12:45, the hour hand has moved due to the 45 minutes. Each minute, the hour hand moves 0.5 degrees (30 degrees / 60 minutes). Therefore, at 45 minutes, the hour hand is at 0 + (45 * 0.5) = 22.5 degrees. Since it is 12:45, we add the 12 hours: 12 * 30 + 22.5 = 337.5 degrees.
Step 4: Find the angle between the hour and minute hands by taking the absolute difference between their positions: |337.5 - 270| = 67.5 degrees.
