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At 3:40, the hour hand and the minute hand of a clock form an angle of
- a)135°
- b)130°
- c)120°
- d)125°
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
At 3:40, the hour hand and the minute hand of a clock form an angle of...
Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at
M
minutes past
H
'o clock
When the minute hand is ahead of the hour hand, the angle between the two hands at
M
minutes past
H
'o clock
Most Upvoted Answer
At 3:40, the hour hand and the minute hand of a clock form an angle of...
To find the angle between the hour hand and the minute hand at 3:40, we need to determine the positions of both hands.
At 3:40, the hour hand will be slightly past the 3 o'clock mark, but not quite at the 4 o'clock mark. To find the exact position, we can calculate how far the hour hand moves in 40 minutes.
Since the hour hand completes a full rotation in 12 hours (720 minutes), it moves 360 degrees in 720 minutes. Therefore, in 40 minutes, the hour hand moves:
(40 minutes) * (360 degrees / 720 minutes) = 20 degrees
So, the hour hand will be 20 degrees past the 3 o'clock mark.
Next, we need to determine the position of the minute hand at 3:40. The minute hand completes a full rotation in 60 minutes, so in 40 minutes, it moves:
(40 minutes) * (360 degrees / 60 minutes) = 240 degrees
Therefore, the minute hand will be 240 degrees past the 12 o'clock mark.
Now, to find the angle between the hour hand and the minute hand, we take the difference between their positions:
240 degrees - 20 degrees = 220 degrees
Therefore, at 3:40, the hour hand and the minute hand of a clock form an angle of 220 degrees.
At 3:40, the hour hand will be slightly past the 3 o'clock mark, but not quite at the 4 o'clock mark. To find the exact position, we can calculate how far the hour hand moves in 40 minutes.
Since the hour hand completes a full rotation in 12 hours (720 minutes), it moves 360 degrees in 720 minutes. Therefore, in 40 minutes, the hour hand moves:
(40 minutes) * (360 degrees / 720 minutes) = 20 degrees
So, the hour hand will be 20 degrees past the 3 o'clock mark.
Next, we need to determine the position of the minute hand at 3:40. The minute hand completes a full rotation in 60 minutes, so in 40 minutes, it moves:
(40 minutes) * (360 degrees / 60 minutes) = 240 degrees
Therefore, the minute hand will be 240 degrees past the 12 o'clock mark.
Now, to find the angle between the hour hand and the minute hand, we take the difference between their positions:
240 degrees - 20 degrees = 220 degrees
Therefore, at 3:40, the hour hand and the minute hand of a clock form an angle of 220 degrees.
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At 3:40, the hour hand and the minute hand of a clock form an angle ofa)135°b)130°c)120°d)125°Correct answer is option 'B'. Can you explain this answer?
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