Answer :

Final answer:

To find the smaller angle between the hour and minute hands at 11:45 AM, calculate the individual angles from the 12 o'clock position for each hand and then determine the absolute difference between them. The smaller angle is 82.5 degrees.

Explanation:

To find the smaller angle between the hour and minute hands of a clock at 11:45 AM, you can follow this step-by-step approach:

  1. Calculate the angle advanced by the hour hand from 12 o' clock. Since the hour hand moves at 360 degrees in 12 hours, it moves 0.5 degrees per minute. At 11:45 AM, the hour hand has moved (11 imes 60 + 45) imes 0.5 = 352.5 degrees from the 12 o'clock position.
  2. The minute hand, on the other hand, moves at 360 degrees in 60 minutes, which is 6 degrees per minute. By 11:45 AM, the minute hand will be at 45 imes 6 = 270 degrees from the 12 o'clock position.
  3. To find the angle between the two hands, subtract the larger angle from the smaller angle, taking the absolute value. Therefore, the smaller angle = |352.5 - 270| = 82.5 degrees.

Note that this method provides the smaller angle directly and is straightforward for computing angles in clock problems.

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