Question

Angle between the minute hand and the hour hand at 5 o’clock.

Answer 1

Hint: First of all this is a very simple and a very easy problem. This problem deals with finding the angle between the chosen sectors. We know that a clock has 12 hour stands, though a day has 24 hours, but we can only see 12 hours on the clock. There is only one hour hand, one minute hand and one second hand in any clock. If it is any x o’clock, then the hour hand is on the x hour stand, whereas the minute hand is on the 12 hour stand.

Complete step-by-step answer:
Given that the time on the clock is 5 o’clock.
Which means that the hour hand is on 5, and minute hand is on 12.
Visualizing the information as given below:

We can see that in the above picture the hour hand is on 5, whereas the minute hand is on 12.
As we know that in the clock there are 12 hour stands.
A circle has an angle ${360^ \circ }$, at the center.
As the hour stands divide the clock into 12 slices or 12 pies or 12 sectors.
The angle taken by each sector is given by:
$ \Rightarrow \dfrac{{{{360}^ \circ }}}{{12}} = {30^ \circ }$
Thus each sector takes ${30^ \circ }$.
The angle taken by each sector is = ${30^ \circ }$
Now when the time is 5 o’clock, there are five sectors between the minute hand and the hour hand.
The number of sectors between the minute hand and the hour hand is = 5
$\therefore $The angle associated with the five sectors is given by the product of five sectors and the angle for each sector, as given below:
$ \Rightarrow 5 \times {30^ \circ }$
$ \Rightarrow {150^ \circ }$
$\therefore $The angle between the minute hand and the hour hand at 5 o’clock is ${150^ \circ }$.

The angle between the minute hand and the hour hand at 5 o’clock is ${150^ \circ }$

Note:
Please note that while finding the angle between the minute hand and the hour hand at 5 o’clock, there is a chance of confusion, here the angle considered is the clockwise direction angle between the minute and the hour hand, but not the anti-clock wise direction angle. The anti-clock wise direction angle between the minute hand and the hour hand is ${210^ \circ }$, which is wrong, so please be careful while solving this problem.