If a clock shows 3:15, what is the angle between the hour and the minute hands? (2023)
Practice Questions
1 question
Q1
If a clock shows 3:15, what is the angle between the hour and the minute hands? (2023)
45 degrees
90 degrees
97.5 degrees
75 degrees
At 3:15, the hour hand is at 97.5 degrees (3*30 + 15*0.5) and the minute hand is at 90 degrees (15*6). The angle between them is 97.5 - 90 = 7.5 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: If a clock shows 3:15, what is the angle between the hour and the minute hands? (2023)
Solution: At 3:15, the hour hand is at 97.5 degrees (3*30 + 15*0.5) and the minute hand is at 90 degrees (15*6). The angle between them is 97.5 - 90 = 7.5 degrees.
Steps: 7
Step 1: Understand that the clock has 12 hours and each hour represents 30 degrees (360 degrees / 12 hours).
Step 2: Calculate the position of the hour hand. At 3:00, the hour hand is at 3 * 30 = 90 degrees.
Step 3: Since it's 3:15, the hour hand moves further. It moves 0.5 degrees for each minute (30 degrees / 60 minutes).
Step 4: Calculate the additional movement of the hour hand for 15 minutes: 15 * 0.5 = 7.5 degrees.
Step 5: Add the additional movement to the hour hand's position: 90 degrees + 7.5 degrees = 97.5 degrees.
Step 6: Calculate the position of the minute hand. At 15 minutes, the minute hand is at 15 * 6 = 90 degrees.
Step 7: Find the angle between the hour and minute hands by subtracting the smaller angle from the larger angle: 97.5 degrees - 90 degrees = 7.5 degrees.
