A clock shows 8:00. What will be the angle between the hour and minute hands at 8:30?
Practice Questions
1 question
Q1
A clock shows 8:00. What will be the angle between the hour and minute hands at 8:30?
180 degrees
165 degrees
150 degrees
135 degrees
At 8:30, the hour hand is at 255 degrees (8 * 30 + 30 * 0.5) and the minute hand is at 180 degrees (30 * 6). The angle between them is |255 - 180| = 75 degrees.
Questions & Step-by-step Solutions
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Q
Q: A clock shows 8:00. What will be the angle between the hour and minute hands at 8:30?
Solution: At 8:30, the hour hand is at 255 degrees (8 * 30 + 30 * 0.5) and the minute hand is at 180 degrees (30 * 6). The angle between them is |255 - 180| = 75 degrees.
Steps: 9
Step 1: Understand that a clock has two hands: the hour hand and the minute hand.
Step 2: Know that the hour hand moves 30 degrees for each hour (360 degrees / 12 hours = 30 degrees per hour).
Step 3: Calculate the position of the hour hand at 8:30. At 8:00, the hour hand is at 8 * 30 = 240 degrees.
Step 4: The hour hand also moves as the minutes pass. It moves 0.5 degrees for each minute (30 degrees / 60 minutes = 0.5 degrees per minute).
Step 5: Since it is 30 minutes past 8:00, the hour hand moves an additional 30 * 0.5 = 15 degrees.
Step 6: Add the movement of the hour hand to its position at 8:00: 240 degrees + 15 degrees = 255 degrees.
Step 7: Now, calculate the position of the minute hand at 8:30. The minute hand moves 6 degrees for each minute (360 degrees / 60 minutes = 6 degrees per minute).
Step 8: At 30 minutes, the minute hand is at 30 * 6 = 180 degrees.
Step 9: To find the angle between the hour and minute hands, subtract the smaller angle from the larger angle: |255 - 180| = 75 degrees.
