Time and angle measures are one of the important types of mathematical problems. We all know that time problems (clock angle measure problem) are all about finding the angles between the hands (Hands are minute hand or hour hand or second hand) of an analog clock. This is very important part of geometry. In geometry the measurement unit for angle is the “Degree”. A circle is divided into 360 equal degrees. Moreover, degrees are divided into two terms, known as Minutes and Seconds. This division of degree is not universal. (To get help on central board of secondary education books click here)
These problems generally relate to two different measures which are angles and time. For such problems we always consider the change rate of the angle in degree per minute (deg/min) and we may also use arc lengths in this. In an analog clock the hour hand of the clock turns 360 degree in 12 hours which are 720 minutes or we can say 0.5 degree per minute. In the same analogue clock the minute hand turns 6 degree per minute or 360 deg in 1 hour (60 minutes).
Now to solve related problems we need to apply some formulas in form of general equations. These equations are:
1. Equation for angle of the hour hand of the clock:
Ahr = ½ Me = ½ ( 60 H + M)
Here Ahr is the angle of the hand measured clockwise from the exact time 12’o clock. M is the minute past hour and Me is minute past 12’o clock.
2. Equation for degree on minute hand of the clock:
Amin = 6*M
Where Amin is the angle of the hand measured clockwise from the time 12’o clock and its unit is degree.
For example: Time given is 5:30 then the angle of hour hand in degrees:
Ahr = ½(60*5 + 30) =165 degree
Similarly for the same time the angle of minute hand in degree:
Amin = 6*30 = 180 degree.
So today we learnt about Times and Angle measures. In the next session I will tell you about arc lengths and In the next session we will discuss about Rate, distance in geometry.
These problems generally relate to two different measures which are angles and time. For such problems we always consider the change rate of the angle in degree per minute (deg/min) and we may also use arc lengths in this. In an analog clock the hour hand of the clock turns 360 degree in 12 hours which are 720 minutes or we can say 0.5 degree per minute. In the same analogue clock the minute hand turns 6 degree per minute or 360 deg in 1 hour (60 minutes).
Now to solve related problems we need to apply some formulas in form of general equations. These equations are:
1. Equation for angle of the hour hand of the clock:
Ahr = ½ Me = ½ ( 60 H + M)
Here Ahr is the angle of the hand measured clockwise from the exact time 12’o clock. M is the minute past hour and Me is minute past 12’o clock.
2. Equation for degree on minute hand of the clock:
Amin = 6*M
Where Amin is the angle of the hand measured clockwise from the time 12’o clock and its unit is degree.
For example: Time given is 5:30 then the angle of hour hand in degrees:
Ahr = ½(60*5 + 30) =165 degree
Similarly for the same time the angle of minute hand in degree:
Amin = 6*30 = 180 degree.
So today we learnt about Times and Angle measures. In the next session I will tell you about arc lengths and In the next session we will discuss about Rate, distance in geometry.
No comments:
Post a Comment