Acute angle it is less than 90degree
The angle formed by the clock's hands at 11:40 is either 110 degrees or 250 degrees, representing the smaller and larger angles formed between the hands.
To find the angle formed by the hands of a clock at 11:40, we need to calculate the angles for both the hour and the minute hands from the 12 o'clock position.
The minute hand at 40 minutes is two-thirds of the way through its cycle, as it takes 60 minutes for a full rotation. This means the minute hand is at 240 degrees (40 minutes / 60 minutes * 360 degrees).
For the hour hand at 11 o'clock, it has traveled most of the way through its cycle, which is 12 hours long. By 11:40, the hour hand has moved beyond the 11 o'clock mark. The hour hand moves 0.5 degrees per minute (30 degrees per hour / 60 minutes per hour). So, at 11:40, the hour hand has moved 11 hours * 30 degrees/hour + 40 minutes * 0.5 degrees/minute = 330 degrees + 20 degrees = 350 degrees from the 12 o'clock position.
To find the angle between the hour and minute hands, we subtract the smaller angle from the larger one. This can be done in two ways as the hands can form an angle less than or greater than 180 degrees. The smaller angle is 350 degrees - 240 degrees = 110 degrees. The larger angle, going the other way around the clock, is 360 degrees - 110 degrees = 250 degrees.
Therefore, the angle between the hour and minute hands at 11:40 is either 110 degrees or 250 degrees, depending on whether you want the smaller or larger angle.
At 11:40, the angle formed by the clock hands is either 110 degrees or 250 degrees, with 110 degrees being the smaller angle. The minute hand points at 240 degrees and the hour hand at 350 degrees from the 12 o'clock position. The calculation of their positions leads to these angles based on their movement rates.
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