Question

How is $1$ degree equal to \[60\] minutes?

Answer 1

Hint: Earlier, the Babylonian sexagesimal number system was used which had a base $60$ lead to the invention of time and angular conventions and the relationship between them. The revolution of the earth and the time taken for a single revolution of earth is required to be considered. The concept of standard conversions of time and the division of a circle with respect to angles that is measured in degrees is applied in order to determine the relation between degree and minutes.

Complete step by step answer:
The clocks which we use in our daily life are of great significance. The principle behind the hours, minutes and seconds hands of the clock comes from the concept that since the clock is shaped like a circle, the circle is divided into a number of equal parts or sections using which we calculate the hour, minutes and seconds.

Since the clock is said to be a full circle, the arc of the circle, that is, an hour was divided into \[60\] equal parts in order to measure the time in minutes. Similarly, in order to measure the time in seconds the minutes were further divided into \[60\] more equal parts known as seconds. Thus, the relationship between the hour, minute and second quantities were established.The time conventions were as follows:
$1\,hr = 60\,min \\
\Rightarrow 1\,min = 60\,sec$

Same way, by the DMS notation which stands for degree-minute-seconds it was proved that there exists a relationship between degree and minutes as well. This notation was used for many conversions and calculations. Just like how there was a relation between the hour, minute and second quantities, there was said to be a relation between degrees and minutes.

Now, in order to determine the relation between the degrees and minute quantities we need to take into consideration the concept of the revolution of the Earth. It is already known to us that the Earth revolves around the sun and hence there is a variation in the time of the day. We also know that it takes $24$ hours for the Earth to complete one revolution around its own axis and this corresponds to one day for us. Hence we know that,
$1\;day = 24\;hours$

By taking the geometry of the clock which is said to be circular in shape, we can say that in order to obtain a complete circle a ${360^ \circ }$ arc must be drawn. We will now consider only the hour hand of the clock. We know that a day starts from $12:00$ midnight. If we consider the hour hand to start from $12$ midnight, that is, the number twelve in the clock, we can say that the hour hand of the clock is said to move or complete sweeping through the entire arc of the circle two times in a period of $24$ hours which is said to be one day.

Once, when it strikes noon and once when it strikes $12:00$ midnight in order to complete the current day and start the day correspondingly. The hour hand is said to trace the ${360^ \circ }$ arc of the clock two times and this means that it completes two circles in one day and hence the total will be:
$ \Rightarrow 2 \times 360$
There are $12$ divisions in a clock and hence for a single division we get:
${1^ \circ } = \dfrac{{2 \times 360}}{{12}}$ minutes
By solving out this expression we get:
$\therefore {1^ \circ } = 60$ minutes

Hence the relation that $1$ degree is equivalent to $60$ minutes is determined.

Note: There is often a misconception that $1$ degree is equivalent to \[4\] minutes instead of \[60\] minutes which is wrong. This is because when taking the ${360^ \circ }$ rotation of the Earth into consideration, calculations lead to the conclusion that the Earth takes around \[4\] minutes to rotate an angle of ${1^ \circ }$. Hence, this does not affect the relation that $1$ degree equals \[60\] minutes and hence this relation is proved to be correct.