Find the acute angle formed by the hour and minute hand of a clock at 6h 22 min

Expert Answers
justaguide eNotes educator| Certified Educator

The acute angle between the hour and minute hands of a clock at 6 h 22 minutes has to be determined.

At 12:00 the angle between the two hands is 0.

In 6 hours 22 minutes the hour hand moves by an angle` 6*(360/12) + (22/60)*(360/12) = 191` degrees from the position at 12:00.

In 6 hours 22 minutes, the minute hand moves by an angle equal to `(22/60)*360` = 132 degrees from its position at 12:00.

The angle between the two hands of the clock at 6:22 is 191 - 132 = 59 degrees.

michuraisin | Student

At 6:22, the minute hand would be around 4, while the hour hand would be around 6. This is the span we are trying to measure. To solve this problem, I would imagine the clock as a circle composed of degrees, rather than numbers representing time. Knowing that there are 360 degrees in a circle, and 12 hours on a clock, each hour would represent 30 degrees. Assuming that the number 12 represents both degree 0 and 360, this would mean the minute hand is around 120 degrees and the hour hand around 160 degrees.

To find the exact location of the minute hand, simply calculate (22/60)*360. This leads to the minute hand being at 132 degrees.

Since it's nearly half past 6, the hour hand also has to be close to halfway towards 7. If we take 22/60th of 30 degrees (since each hour is 30 degrees), then we know that the minute hand is 11 degrees past 180 degrees. 180+11 is 191, thus the location of the hour hand.

Now, simply do 191-132, and the angle of the hands at 6:22 is 59 degrees!