At 12 o’clock, the minute hand and the hour hand of the clock overlap, so the angle between them is zero. This is because the hour hand is pointing straight up at the 12, while the minute hand is at the same position as the hour hand.

To understand this better, we need to remember some basics about clocks. A clock has two hands that rotate around its center: the hour hand and the minute hand. The hour hand is shorter and moves slowly, while the minute hand is longer and moves faster. They both start at the 12 o’clock position and move in a circular motion.

Let’s assume that the hour hand moves one complete rotation in 12 hours, while the minute hand moves one complete rotation in 60 minutes. This means that in one minute, the minute hand moves 1/60th of a full rotation, which is 6 degrees. In one hour, the hour hand moves 1/12th of a full rotation, which is 30 degrees.

Now, if we go back to the question, we can see that at 12 o’clock, the hour hand and the minute hand are at the same position. The hour hand has completed half a rotation (180 degrees) from its starting position, while the minute hand has completed a full rotation (360 degrees).

To calculate the angle between them, we need to find the difference in their position. Since the hour hand has covered 180 degrees and the minute hand has covered 360 degrees, we can subtract the angle covered by the hour hand from the angle covered by the minute hand. This gives us:

360 degrees – 180 degrees = 180 degrees

So the angle between the hands of the clock at 12 o’clock is 180 degrees. However, as mentioned earlier, they overlap at this position, so the angle between them is actually zero.

The angle between the hands of the clock at 12 o’clock is zero because they are overlapped at this position. However, if we consider their positions just before or just after 12 o’clock, the angle between them is 180 degrees.

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## At what time between 12.00 and 1.00 angle of the hands is O degrees?

To determine the time when the angle between the hands of a clock is zero degrees between 12.00 and 1.00, we first need to understand the movement of the clock hands on a standard 12-hour clock. The hour hand moves at a slower pace than the minute hand and completes a full rotation every 12 hours, while the minute hand completes a full rotation every 60 minutes or 1 hour.

At exactly 12.00 (noon), the hour hand is pointing directly at the 12, and the minute hand is pointing at the 12 as well. At this point, the angle between the two hands is zero degrees. As time progresses, the minute hand moves around the clock face at a constant pace, while the hour hand moves more slowly, taking 12 hours to make a full rotation.

To calculate the time when the angle between the hands is zero degrees for the first time after noon, we need to determine how far the hands will move relative to each other during that time. Since the minute hand moves at a steady pace of 12 degrees per minute (360 degrees divided by 60 minutes), we know it will move 12/60 or 1/5 of a degree in one second.

The hour hand, meanwhile, moves at a slower pace of only 1/2 degree per minute (30 degrees divided by 60 minutes).

Therefore, for the angle between the hands to be zero degrees, the minute hand needs to move ahead the hour hand by 30 degrees, which is the difference between zero degrees and 30 degrees, the angle between the hands at noon. To calculate the time it takes for the minute hand to move 30 degrees ahead of the hour hand, we can use the following formula:

t = (30 – 0.5H) / 11/6

Where:

t is the number of minutes past noon

H is the hour hand position in hours (0≤ H≤ 12)

Plugging in H = 12 (since the hour hand is pointing at the 12 at noon), we get:

t = (30 – 0.5 x 12) / 11/6

t = 30 / 11/6

t ≈ 6.55 minutes

Therefore, the time at which the angle between the hands is zero degrees for the first time after noon is approximately 6.55 minutes past 12.00. We can check this result by calculating the position of the hour and minute hands at that time. Since the minute hand moves at a constant pace of 12 degrees per minute, it will have moved 12 x 6.55 = 78.6 degrees from its position at noon.

The hour hand, meanwhile, will have moved (6.55 / 60) x 30 = 3.27 degrees from its position at noon. The angle between the hands is then:

θ = |30H – 11/2M|

θ = |30 x 12 – 11/2 x (78.6 + 3.27)|

θ ≈ 0 degrees

As we can see, the angle between the hands is indeed zero degrees at approximately 6.55 minutes past 12.00. However, it is important to note that this is not the only time when the angle between the hands is zero between noon and 1.00. In fact, there is a second time, just before 1.00, when the angle between the hands is zero again.

To determine this time, we can use the same formula as before but with H = 1:

t = (30 – 0.5 x 1) / 11/6

t ≈ 5.45 minutes

Therefore, the time just before 1.00 when the angle between the hands is zero is approximately 5.45 minutes before 1.00. Again, we can check this result by calculating the position of the hour and minute hands at that time:

Minute hand: 12 x (60 – 5.45) = 694 degrees

Hour hand: 1/2 x (60 – 5.45) = 27.78 degrees

Angle between the hands: |30 – 11/2 x (694/360) + 27.78| ≈ 0 degrees

There are two times between noon and 1.00 when the angle between the hands of a clock is zero degrees. The first time is approximately 6.55 minutes past noon, and the second time is approximately 5.45 minutes before 1.00.

## What time is 12 to 1 o’clock the hands of clock coincide?

The hands of the clock coincide twice a day – once during the day and once at night. When the clock reads 12:00 PM or noon, the minute and hour hands coincide, forming a straight line. This is because at noon, the hour hand would have moved precisely 360 degrees (12 hours x 30 degrees per hour), and the minute hand would be placed exactly at the 12 o’clock position.

Similarly, when the clock reads 12:00 AM or midnight, the minute and hour hands also coincide, forming a straight line. At midnight, the hour hand would be pointing precisely at the 12 o’clock position, having completed one full rotation of 360 degrees from the time it was at the same position 12 hours ago.

The minute hand would also be positioned at the 12 o’clock position, indicating the start of a new day.

Therefore, the hands of the clock coincide twice a day – once at 12:00 PM (noon) and once at 12:00 AM (midnight). These two instances are the only times during a 24-hour period when the clock hands will align with each other in a straight line.

## How do you find the angle between clocks?

To find the angle between clocks, you need to follow a few simple steps. The angle between clocks gives you the difference in the time between two clocks.

Step 1: Determine the time on both clocks.

Before you can find the angle between clocks, you need to determine the time on both clocks. Ensure both clocks are set to the same time zone.

Step 2: Calculate the difference in time.

Once you have the time on both clocks, you need to calculate the difference between them. For example, if one clock shows 2:00 PM and the other shows 6:00 PM, the difference in time is 4 hours.

Step 3: Convert the difference in time to degrees.

To convert the difference in time to degrees, you need to know that a full circle is 360 degrees, and there are 24 hours in a day. You can use the formula (360/24) = 15 to convert the hours to degrees. In our example, the difference in time is 4 hours, so 4 x 15 = 60 degrees.

Step 4: Determine the direction of the angle.

You also need to determine the direction of the angle. If the second clock is ahead of the first clock, the angle is positive. If the second clock is behind the first clock, the angle is negative. In our example, the second clock is ahead of the first clock, so the angle is positive.

Step 5: Calculate the final angle.

To calculate the final angle, you simply multiply the degrees by the direction. In our example, the angle is +60 degrees.

Finding the angle between clocks requires knowing the time on both clocks, calculating the difference in time, converting the difference to degrees, determining the direction of the angle, and calculating the final angle.

## How many times are the hands of a clock at right angles in 12 hours 1 24 times 2 48 times 3 22 times 4 44 times?

The question asks how many times the hands of a clock are at right angles in a period of 12 hours. To answer this question, it is important to understand what is meant by the term “right angles.” Two lines or geometric shapes are said to be at right angles if they intersect each other and create a 90-degree angle at the point of intersection.

In the case of a clock, the hands are two lines that intersect at the center of the clock face. The minute hand moves 360 degrees around the clock face in one hour, while the hour hand moves at a slower pace, covering 30 degrees in one hour. With this information, we can determine when the hands are at right angles to each other.

Let’s first look at the possible positions of the hands. At 12 o’clock, the hour hand points directly up while the minute hand points straight down. At 3 o’clock, the hour hand points to the right while the minute hand points straight down. At 6 o’clock, the hour hand points straight down while the minute hand points directly up.

At 9 o’clock, the hour hand points to the left while the minute hand points straight up.

To be at right angles, the two hands have to be positioned so that they create a 90-degree angle. This can be achieved in several ways, but most commonly, it happens when the minute hand and the hour hand are 15 minutes apart from each other. For example, at 3:15, the minute hand is at the 3 o’clock position while the hour hand has moved 15 degrees past the 3 o’clock position, creating a 90-degree angle between them.

Using this information, we can determine how many times the hands of a clock are at right angles in 12 hours. In each hour, there are two possible times when the hands are at right angles, which gives us a total of 24 possible times in 12 hours. However, some of these times overlap, such as 1:30 and 10:30, both of which have the hands at right angles.

Therefore, we need to eliminate the duplicates to get an accurate count.

After eliminating the duplicates, we are left with a total of 22 times when the hands of a clock are at right angles in 12 hours. Therefore, the correct answer to the question is option 3: 22 times.

## What is the clock angle formula?

The clock angle formula is a mathematical formula used to calculate the angle between the hour and minute hands of a clock. The formula is based on the fact that the hour hand moves 30 degrees for every hour and the minute hand moves 6 degrees for every minute.

The formula can be represented as follows:

Angle = |30H – 11/2M|

Where H is the hours and M is the minutes. The absolute value sign is used to ensure that the angle is always positive, regardless of which hand is ahead of the other.

For example, if the time on a clock is 9:15, we can use the formula to calculate the angle between the hour and minute hands as follows:

H = 9

M = 15

Angle = |30 x 9 – 11/2 x 15|

Angle = |270 – 82.5|

Angle = 187.5 degrees

Therefore, the angle between the hour and minute hands on a clock that reads 9:15 is 187.5 degrees.

The clock angle formula is useful in solving various problems related to time and clocks, such as calculating the earliest and latest time at which the hands of a clock will form a certain angle or determining the time at which the hands of a clock will be at a certain angle. It is a simple yet powerful formula that can be applied to a wide range of clock-related problems.

## What is the angle made by hour hand in 12 minutes?

The hour hand of a clock takes 12 hours to complete one revolution, which means it moves 360 degrees in 12 hours. Therefore, the hour hand moves 30 degrees in one hour (360/12 = 30).

Since we are asked about the angle made by the hour hand in 12 minutes, we can simply calculate the fraction of the hour it has moved in that time. 12 minutes is equal to 1/5th of an hour, or 0.2 hours (60 minutes per hour = 60/12 = 5 minutes per hour, so 12 minutes = 12/60 = 1/5th of an hour).

Multiplying 30 degrees by 0.2 gives us the total degree angle the hour hand moves in 12 minutes, which is 6 degrees. Therefore, the angle made by the hour hand in 12 minutes is 6 degrees.