Figure 701 : Clock - Angle between two hands
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Q01 |
- Diagram : Clock - Angle between two hands
- Q02 | - Angle of short hand
- Q03 | - Angle of minute hand
- Q04 | - Time when hour hand and minute hand have 180 degrees angle
- Q05 | - Angle of hour hand when two hands make 180 degree angle
- Q02 | - Angle of short hand
Q01. Diagram : Angle between two hands
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Q02. Angle of hour hand
Definition
- Each hour = 360 degrees/12
- Angle of hour hand relative to 12 o'clock
- 1 o'clock = 30 degrees
- 2 o'clock = 60 degrees
- 3 o'clock = 90 degrees
- 4 o'clock = 120 degrees
- 5 o'clock = 150 degrees
- 6 o'clock = 180 degrees
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Q03. Angle of minute hand
Definition
- Each minute = 360 degrees/60 = 6 degrees
- Angle of minute hand relative to 12 o'clock position
- At 1 minute = 6 degrees
- At 15 minute = 90 degrees
- At 30 minute = 180 degrees
- At 45 minute = 270 degrees
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Q04. Angle between two hands
Time when two hands two hands make 180 between 3 and 4 o'clock
- Let hour = x
- Let minute = y
- The time is x + y/60
- Hence angle of short hand = (x + y/60)*30
- Hence angle of minute hand = 6*y
- Since two hands are coincided
- Hence (x + y/60)*30 = 6*y - 180
- Hence y = (30*x + 180)/(6 - 0.5)
- Between 3 and 4 o'clock, x = 3
- Hence y = (90 + 180)/5.5 = 49.09 minutes
- Hence the time is 3 o'clock 49.09 minutes
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Q05. Angle of hour hand when hour hand and minute hand coincide
Angle of short hand when two hands coincide between 3 and 4 o'clock
- Let hour = x
- Let minute = y
- The time is x + y/60
- Hence angle of short hand = (x + y/60)*30
- Hence angle of minute hand = 6*y
- Since two hands are coincided
- Hence (x + y/60)*30 = 6*y
- Hence (x + y/60)*30 = 6*y - 180
- Hence y = (30*x + 180)/(6 - 0.5)
- Between 3 and 4 o'clock, x = 3
- Hence y = (90 + 180)/5.5 = 49.09 minutes
- Hence the time is 3 o'clock 49.09 minutes
- Short hand at (3 + 49.09/60)*30 = 114.54 degrees
- Long hand at 49.09*6 = 294.54
- Angle between two hands = 294.54 - 114.54 = 180 degrees
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