Clock Aptitude Reasoning Tricks & Problems - Finding Angle Between The Hands of a Clock Given Time

The Organic Chemistry Tutor
24 Aug 201712:18
EducationalLearning
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TLDRThe video script provides a detailed explanation of how to calculate the angle between the hour and minute hands of an analog clock at various times. It begins with a step-by-step guide for the time 12:30, illustrating the process of determining the position of both hands and the angles involved. The script then extends the method to other times, such as 12:00 and 10:25, using fractions to represent the hour hand's position between two numbers. It also covers the calculation of both the shortest and longest angles between the hands. The explanation includes visual aids like drawings and emphasizes the importance of understanding the relationship between hours, minutes, and degrees in a full circle.

Takeaways
  • 🕒 The angle between the minute and hour hands on a clock can be calculated based on the time shown.
  • 📏 Each hour on the clock represents an angle of 30 degrees, as a full circle is 360 degrees and there are 12 hours.
  • ⏱ At 12:30, the minute hand is at 6 and the hour hand is halfway between 12 and 1, creating an angle of 165 degrees between the hands.
  • 🔢 To find the angle for a specific time, determine the fraction of the hour that has passed and calculate the corresponding angle in degrees.
  • 📉 For times like 1:20, the hour hand is one-third of the way from 1 to 2, which translates to an angle of 20 degrees from the 1 o'clock position.
  • 📈 The total angle between the hands at 1:20 is 80 degrees, obtained by adding the angles between the hour numbers and the fractions of the hour.
  • 🕚 At 11:15, the minute hand is at 3 and the hour hand is one-fourth of the way from 11 to 12, resulting in an angle of 112.5 degrees between the hands.
  • 🔠 For the time 10:25, the minute hand is at 5 and the hour hand is slightly past 10, with the angle between the hands being 162.5 degrees, the shorter angle.
  • 🔄 To find the longer angle at 10:25, subtract the shorter angle from 360 degrees, yielding an angle of 197.5 degrees.
  • 📌 The shortest angle between the hour and minute hands is always less than 180 degrees, as the hands cannot form a straight line at any given time.
Q & A

  • At 12:30, what is the position of the minute hand on an analog clock?

    -At 12:30, the minute hand, which is the long hand, is pointing directly at the 6 on the clock face.

  • How does the position of the hour hand change between 12:00 and 12:30 on an analog clock?

    -Between 12:00 and 12:30, the hour hand moves from the 12 towards the 1, but it is exactly halfway between 12 and 1 at 12:30.

  • What is the angle between the hour hand and the minute hand at 12:30?

    -The angle between the hour hand and the minute hand at 12:30 is 165 degrees.

  • How is the angle between the hour hand and the minute hand at 12:30 calculated?

    -The calculation involves understanding that each hour represents 30 degrees. At 12:30, the hour hand is halfway between 12 and 1, which is 15 degrees from the 12. Adding the 150 degrees from 12 to 6 gives a total angle of 165 degrees.

  • What is the angle between the hour hand and the minute hand at 1:20?

    -At 1:20, the minute hand is at 4, and the hour hand is two-thirds of the way between 1 and 2, resulting in an angle of 80 degrees between the two hands.

  • How can you determine the position of the hour hand at a given time?

    -To determine the position of the hour hand, you can use the minute value divided by 60 to find the fraction of how far it is from one of the hours. The remaining fraction represents the distance from the next hour.

  • What is the shortest angle between the hour and minute hands at 10:25 on an analog clock?

    -The shortest angle between the hour and minute hands at 10:25 is 162.5 degrees.

  • How do you find the shortest angle between the hour and minute hands on an analog clock?

    -To find the shortest angle, calculate the angles between the hour and minute hands and the 12 o'clock position, then subtract the smaller angle from 180 degrees or add the smaller angle to the larger one to find the shortest angle.

  • What is the angle between the hour hand and the minute hand at 11:15 on an analog clock?

    -At 11:15, the angle between the hour hand and the minute hand is 112.5 degrees.

  • How can you convert the time on an analog clock to degrees?

    -To convert time to degrees, first determine the positions of the hour and minute hands on the clock face, then calculate the angles between these positions using the fact that each hour represents 30 degrees.

Outlines
00:00
🕒 Understanding Clock Angles at 12:30

This paragraph explains how to calculate the angle between the hour and minute hands of an analog clock at 12:30. It starts by establishing that each hour on the clock represents 30 degrees, as the clock completes a 360-degree rotation in 12 hours. At 12:30, the minute hand points at the 6, while the hour hand is halfway between 12 and 1. The calculation involves determining the angle from 1 to 6 (150 degrees) and then finding the half-hour angle (15 degrees) because the hour hand is between 12 and 1. The final angle between the hands is the sum of these, which is 165 degrees. This is a step-by-step guide to understanding the relationship between time and angles on a clock face.

05:00
🕒 Calculating Clock Angles for 12:00 (120 Degrees)

The second paragraph delves into calculating the angle between the clock hands when the time is represented as 120 degrees, which corresponds to 1:40 on an analog clock. The explanation begins with drawing the clock face and identifying the positions of the hour and minute hands. The hour hand is between 1 and 2, and the minute hand is at the 4, representing 40 minutes past the hour. The calculation involves determining the fraction of the hour that has passed (two-thirds, since 40 minutes is two-thirds of the way to the next hour) and converting this fraction into degrees (20 degrees, which is two-thirds of 30 degrees). The total angle is found by adding the angles between the hour marks (30 degrees each) and the calculated angle, resulting in an 80-degree angle between the hands.

10:03
🕒 Finding Angles at 11:15 and 10:25

The final paragraph presents methods to find the angles between the clock hands at 11:15 and 10:25. For 11:15, the minute hand is at 3, and the hour hand is between 11 and 12. The calculation uses the fraction of the hour that has passed (one-fourth) to determine the hour hand's position and then calculates the angle as 112.5 degrees. For 10:25, the minute hand is at 5, and the hour hand is between 10 and 11. The calculation involves finding the fraction of the hour passed (five-twelfths) and determining the angles between the hour hand and both 10 and 11. The shorter angle, which is less than 180 degrees, is calculated to be 162.5 degrees. The longer angle can be found by subtracting the shorter angle from 360 degrees, resulting in 197.5 degrees. This paragraph provides a comprehensive approach to solving for clock angles at given times.

Mindmap
Keywords
💡Analog Clock
An analog clock is a timekeeping device that uses a rotating dial with hour and minute hands to indicate the time. In the video, the analog clock is the central object of study, as the script discusses how to calculate the angles between the clock hands at various times. The concept is used to explain the positions of the hands at 12:30, 12:00, and other times, illustrating the fundamental principle behind reading an analog clock.
💡Minute Hand
The minute hand is the longer hand on an analog clock that moves to indicate the minutes. It is mentioned in the script as being at the 'six' position at 12:30, signifying the 30 minutes past the hour. The minute hand's position is crucial in calculating the angle with the hour hand, as it directly affects the outcome of the calculation.
💡Hour Hand
The hour hand, also known as the short hand, indicates the hours on an analog clock. The script explains that at 12:30, the hour hand is not exactly at 12 but rather between 12 and 1, which is essential for determining the angle between the hour and minute hands. The hour hand's position is dynamic and changes throughout the day, affecting the angle calculation.
💡Angle
The angle is the measure of rotation between two points, in this case, between the hour and minute hands of a clock. The script focuses on calculating these angles at different times, such as 12:30 and 10:25. The concept of angle is central to the video's theme, as it is used to determine the spatial relationship between the clock hands.
💡Degrees
Degrees are units used to measure angles. The script uses degrees to quantify the angles between the clock hands, such as stating that one hour represents an angle of 30 degrees. The concept of degrees is integral to the calculations performed in the video, providing a numerical value to the angles formed by the clock hands.
💡12:30
The time 12:30 is used as an example in the script to illustrate the process of calculating the angle between the clock hands. At this time, the minute hand is at the six, and the hour hand is halfway between 12 and 1, which helps in determining the angle as 165 degrees. This example is crucial for understanding how to apply the principles discussed in the video.
💡Fraction
A fraction is used in the script to represent the portion of an hour that has passed. For instance, the hour hand's position at 12:30 is described as being halfway (or one-half) between the 12 and 1. Similarly, at 10:25, the fraction of the hour that has passed is five-twelfths. Fractions are essential in determining the exact position of the hour hand and, consequently, the angle between the hands.
💡Shortest Angle
The shortest angle refers to the smallest angle between the hour and minute hands on a clock. In the script, the concept is used when calculating the angle at 10:25, where the goal is to find the angle less than 180 degrees. The shortest angle is significant because it represents the most direct path between the two hands.
💡360 Degrees
A full circle or revolution of the clock hands is 360 degrees. The script mentions that 12 hours on a clock correlate to 360 degrees, making each hour represent 30 degrees. This understanding is fundamental to calculating the angles between the clock hands at any given time.
💡Example Calculation
The script provides several example calculations to demonstrate how to find the angle between the clock hands at different times. These examples, such as the calculations for 12:30 and 10:25, serve to illustrate the process and help viewers understand the method of determining angles on an analog clock.
Highlights

At 12:30, the minute hand is at 6 and the hour hand is between 12 and 1.

The hour hand at 12:30 is exactly in the middle between 12 and 1.

Each hour on the clock represents an angle of 30 degrees.

The angle between the hour hand and minute hand at 12:30 is calculated to be 165 degrees.

For the time 12:00, the angle between the hour and minute hands would be 180 degrees, which is impossible.

To find the angle at 2:40, the hour hand is between 2 and 3, and the minute hand is at 4.

The hour hand at 2:40 is two-thirds of the way from 2 to 3.

The angle between the hour and minute hands at 2:40 is 80 degrees.

At 11:15, the minute hand is at 3 and the hour hand is between 11 and 12.

The hour hand at 11:15 is one-fourth of the way from 11 to 12.

The angle between the hour and minute hands at 11:15 is 112.5 degrees.

For 10:25, the minute hand is at 5 and the hour hand is between 10 and 11.

The hour hand at 10:25 is five-twelfths of the way from 10 to 11.

The shortest angle between the hour and minute hands at 10:25 is 162.5 degrees.

The longer angle at 10:25, if needed, can be found by subtracting the shorter angle from 360 degrees.

All angles on a clock face must add up to 360 degrees.

Transcripts

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