What is the angle between the hour hand and minute hand of a clock at 2:37 p.m?
each minute mark is 1/60 of a circle for the minute hand: 6°
So, the minute hand has gone 37*6 = 222° around.
In the meantime, the hour hand, starting at 2:00 (60° along its path), has advanced another 37/60 * 1/12 = 37/720 of a circle. So, the hour hand has moved 60+(37/2) = 78.5°
Thus, the angle between the hands is 222-78.5 = 143.5°
Great explanation thank you
First comment since 2016 😳
To solve this question, we need to determine the positions of the hour and minute hands on the clock. Here's how we can do that:
1. Hour hand position:
- In a 12-hour clock, the hour hand completes a full rotation every 12 hours or 360 degrees.
- At 2:37 p.m., the hour hand would have moved past the 2 o'clock mark but not yet reached the 3 o'clock mark.
- Since there are 60 minutes in an hour, it moves 1/12th of the way between each hour mark for every 5 minutes passed.
- At 2:37 p.m., the hour hand would have moved 37 minutes past the 2 o'clock mark, which is approximately 37/60 * (1/12 * 360) degrees.
2. Minute hand position:
- In a clock, the minute hand completes a full rotation every 60 minutes or 360 degrees.
- At 2:37 p.m., the minute hand would have moved 37 minutes past the 12 o'clock mark, which is approximately 37/60 * 360 degrees.
Now that we have calculated the positions of both the hour and minute hands, we can find the angle between them:
Angle = Absolute value of (Hour hand position - Minute hand position)
Angle = |(37/60 * (1/12 * 360)) - (37/60 * 360)|
Computing this expression will give us the desired angle.