[roro5611235]

Can someone please explain and show me how to figure out the degrees between the hour hand and the minute hand when the time is 1:40.

[md]

What up

The easiest way to do that is by realizing that the clock's circunference has 360 degrees. Divide this by 12 hours marked in the clock and you get 30 degrees for each hour. If the hour hand is at 1 o'clock, that is 30 degrees from the 12 o'clock. If the minute hand is at 40 then that means the hand is pointing at the number 8, which is 30 degrees X 8 = 240 degrees.

The angle between them is from 240 degrees (40 minutes) all the way to 360 degrees (12 o 'clock) + 30 degrees (1 o'clock).
So 150 Degrees is the smallest angle between them.

[roro5611235]

your wrong. i figured it out a couple minutes ago, thanks for attempting. Hint(when the times 1: 40 the hour hand is directly on the 1, its a little past it.

[roro5611235]

*isnt dirctly on the one

[chris]

Find out the degrees between the hour hand and the 12 hour position. Do the same for the minutes hand. Then subtract those two.
_________________
Regards

Chris Karakas
www.karakas-online.de

[md]

Oh right, I see what you are saying roro5611235. You need to see how much the hand that marks the hour has moved by the time the minute hand points at 40 minutes... I overlooked that fact, sorry.

I guess to figure that out you used percentages or rule of three, and after the calculations you realized that the hour hand moves 20 degrees when the minute hand travels 40 minutes.

So to the last answer I gave you that was 150 degrees you add that extra 20 degrees mentioned above. The angle is 170 between them.

Good thing you pointed that out.

[one_time_poster2]

I know the thread is 6 years old but I've got to post.

The general equation is:
Given x hours, where x=0 is the 12th hour, x=1 is the 1st hour, and so on, and given y minutes, the angle between the hour hand and the minute hand is:

| (60x - 11y) / 2 | = | 30x - 5.5y | , where |..| stands for absolute value.


The above equation was found by just taking the degrees between the 12 and the hour hand and subtracting the degrees between the 12 and minute hand.

To find the angle between the 12 and hour hand we first note that each hour is another 30 degrees out. For example, 1 is at 30 degrees, 2 is at 60 degrees, 3 is at 90 degrees, etc. Plus, we need to compensate for the minutes. At 40 minutes, the hour hand will be 40/60 way between x and x+1. The equation looks like this:

30x + (30y/60) for the angle between the 12 and hour hand

and in a similar fashion we can find the minute hand angle:

(360y/60)

Taking the absolute value of the difference gives us the distance.

| 30x + (y/2) + 6y | = | (60x - 11y) / 2 |


Plugging in our example of 1:40, x = 1 and y = 40:
| (60 - 440) / 2 | = | -380 / 2 | = 190 degrees

Another example 3:15, x = 3 and y = 15:
| (180 - 165) / 2 | = | 15 / 2 | = 7.5 degrees


Keep in mind this doesn't always give you the smallest angle. Smallest angle would be:

min(|(60x - 11y) / 2|, 360 - |(60x - 11y) / 2|)