We know that there are 12 divisions in a clock (1 – 12). We also know that there are 360 degrees in a circle. So, the angle between two successive divisions is 360/12 or 30 degrees.
The minute hand covers 30 degrees (1 division) in 5 minutes. Therefore, it’s speed is (30/5) = 6 deg/min.
The hour hand covers 30 degrees (1 division) in 60 minutes. It’s speed is (30/60) = 0.5 deg/min.
Let’s begin with 2:00, since it’s easy to visualize.
At 2:00, the minute hand is at the zeroth degree, while the hour hand is at the 60th degree, i.e. the hour hand is 60 degrees ahead of the minute hand.
In 20 minutes, the minute hand will sweep:
6degmin∗20 min=120 degrees
In 20 minutes, the hour hand will sweep:
0.5degmin∗20 min=10 degrees
However, the hour hand was 60 degrees ahead of the minute hand at the beginning of the hour. So we must add that to get (10 + 60) = 70 degrees.
Therefore, the angle between the minute and hour hand shall be (120 – 70) = 50 degrees.
Step-by-step explanation:
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Answer:
We know that there are 12 divisions in a clock (1 – 12). We also know that there are 360 degrees in a circle. So, the angle between two successive divisions is 360/12 or 30 degrees.
The minute hand covers 30 degrees (1 division) in 5 minutes. Therefore, it’s speed is (30/5) = 6 deg/min.
The hour hand covers 30 degrees (1 division) in 60 minutes. It’s speed is (30/60) = 0.5 deg/min.
Let’s begin with 2:00, since it’s easy to visualize.
At 2:00, the minute hand is at the zeroth degree, while the hour hand is at the 60th degree, i.e. the hour hand is 60 degrees ahead of the minute hand.
In 20 minutes, the minute hand will sweep:
6degmin∗20 min=120 degrees
In 20 minutes, the hour hand will sweep:
0.5degmin∗20 min=10 degrees
However, the hour hand was 60 degrees ahead of the minute hand at the beginning of the hour. So we must add that to get (10 + 60) = 70 degrees.
Therefore, the angle between the minute and hour hand shall be (120 – 70) = 50 degrees.
Step-by-step explanation:
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