During a day, the hour hand and the minute hand of a clock form a right angle, at multiple times. For example, the two hands form a right angle at 9 am. How many times during a day (24 hours) will the two hands form a right angle?
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Step by Step Explanation:
- Let us look at the clock at 9 am:
We can see that the hour hand and the minute hand are making a right angle.
- In a clock, while the minute hand moves, the hour hand also moves, although a lot slowly.
It is easy to see that in a 12 hour period, the minute hand make 12 revolutions while, the hour hand makes one.
We can visualize the above statement this way:
If we hold the clock in our hands and always keep on rotating it slowly, such that the hour hand always stay on the same position, the minute hand will make 12 - 1 = 11 revolutions.
In other words, the minute hand makes 11 revolutions around the hour hand in a 12 hour period.
- For each revolution around the hour hand, the minute hand makes a right angle twice with it. The total number of times we see the two hands making a right angle is 11 × 2 = 22.
- In 12 hours, the number of times the two hands make a right angle = 22
In 24 hours, the number of times the two hands make a right angle = 22 × 2 = 44