find angle between the hands of a clock at 5:15 by Clock Angle Formula

Interview PUZZLE: How many degrees are in the angle between the hour and minute hands of a clock when the time is quarter past 5 i.e. 5:15?

Solution:

We will use simple clock angle formula to solve this problems.

First let’s find how many degrees are in 1 minute of the clock.

Since, minute hand, in 60 minutes covers 360 degree.

Hence, in 1 minute it will cover = 360/60 = 6 degree.

So, the formula is: 1 minute = 6 degree

Since clock time is quarter past 5 i.e. 5:15, let’s calculate the distance covered by hour hand when minute hand covers 15 minute. Using unity Rule:

When Minute hand covers 60 minutes, Hour hand covers 5 minute distance.

When Minute hand covers 1 minutes, Hour hand covers 5/60 minute

If Minute hand covers 15 minute, Hour hand covers (5/60)*15 = 5/4 minute

Result:

Total distance between Minute hand and Hour hand at 5:15 = 10 minute + 5/4 minute

= 45/4 minute.

So, the angle between hour hand and minute hand at 5:15

= 45/4 minute * 6 degree

= 67.5 degree.