Question

What is the angle between minute hand and hour hand at 5 o’clock?

Answer 1

Hint – See the clock nearest to you. Clearly the minute hand will be at 12 and hour hand will be at 5 if it is 5 o’clock. The clock is a circle and a circle has in total ${360^0}$. So the angle between the two hands will be the ratio of their place value multiplied with the total angle constrained within a circle.

Complete step-by-step answer:

As we know at 5 o’clock minute hand is on the 12 number and the hour hand is on the 5 number as shown in figure.

Now as we know that the total number of degrees in a circle is 360.

Therefore the angle formed by the minute hand and hour hand is the ratio of the place value of hour hand to the place value of the minute hand multiplied by 360 degree.

Let the angle between minute and hour hand at 5 o’clock is $\theta $ (see figure).

Therefore angle formed between minute and hour hand at 5 o’clock is
$\theta = \left( {\dfrac{5}{{12}}} \right) \times {360^0} = {150^0}$.

So this is the required value of the angle between minute and hour hand at 5 o’clock.
So this is the required answer.


Note – Such type of questions requires a diagrammatic representation to see the clearer position of the placing of the different hands at that specific time. When the seconds hand revolve a complete ${360^0}$ then the minute hand is shifted one unit clockwise and when the minute rotates complete ${360^0}$ then the hour hand shifts one unit clockwise.