Anonymous
Anonymous asked in Education & ReferenceTrivia · 10 years ago

# what times on the clock are the hands at 180degrees ?

method included

Relevance

This is not as easy as it first appears. One obvious time is 6 o'clock, but the others are not so easy to calculate.

As the minute hand is going around the clock, the hour hand is doing the same but at 1/12 the speed. Therefore when the minute hand gets to 6 (starting from 12 oclock), the hour hand has also moved on so that it is almost half way between the 12 and the 1, and so 12.30 is not at 180 degrees.

In a 12 hour period, the hour hand will have completed one circuit of the clock, and the minute hand 12 circuits. Therefore the minute hand does 11 more circuits than the hour hand. Dividing 1 hour by 11 gives 5 minutes 27.27 seconds. Therefore the hands "pass each other" at 1.05 and 27.27 seconds, 2 10 and 54.54 seconds, 3 16 and 21.81 seconds and so on.

Therefore the first time that the hands are 180 degrees from each other is 12.30 +plus 50% x 5 minutes 27.27 seconds = 12.30+2 mins.43.64 = 12.32 and 43.64 seconds

Then keep adding 1 hour 5 minutes 27.27 seconds for each subsequent time that the hands are at 180 degrees from each other.

12.32 and 43.64 seconds

1.38 and 10.91 seconds

2.43 and 38.18 seconds

3.49 and 5.45 seconds

4.54 and 32.72 seconds

6.00

7.05 and 27.27 seconds

8.10 and 54.54 seconds

9.16 and 21.81 seconds

10.21 and 49.08 seconds

11.27 and 16.35 seconds

please note there are only 11 times per 12 hour period and not 12. Obviously in a 24 hour day, there will be 22 times (the above 11 times with 12 hours added to) in addition to the above times.

• Clock Hands

• only six o'clock. at that point the minute hand is exactly on the twelve, the hour hand is exactly on the six. technically it does happen every hour at times life 3:48:45 as the hour hand moves along with the minuted hand albeit more slowly. six is the only time it happens at an even number

to compensate for the moving hour hand

45/60 = 3/4

3/4 x 5 = 15/4

45 + 15/4 = 48.75 = 48:45 so its 3:48:45

• Anonymous
10 years ago

9:15

&

3:45