The questions asks what is the small angle between clock hands where it shows 11:08
This is not a difficult questions, what I need is the fastest possible solution.
My Solution: We first consider that two hands are on 00:00
I would say an hour is 60 minutes so 360/60 = 6 degree for each minute. Therefore we have 8*6=48 degree for the 08 minutes.
The hour is 11 and is 5*6=30 degree away from 00:00 and we have 30+48=78 degree
BUT, we should also consider that if it's 11:08 then hour hand is moved slightly closer to 00:00 ... but how much? it's that an hour has 60 minutes and (8/60)*6 = 0.8
Therefore the final answer is 78 - 0.8 = 77.2
Is this correct ??? Any faster way???
You are correct until this.
8/60 should be multiplied by 30 degrees, which is the angle between 11 and 12.BUT, we should also consider that if it's 11:08 then hour hand is moved slightly closer to 00:00 ... but how much? it's that an hour has 60 minutes and (8/60)*6 = 0.8
Another way is no notice that the minute hand gains 330 degrees over the hour hand each hour. Since there is 52 minutes between 11:08 and 12:00, the gain is 330 * 52 / 60 = 286 degrees. So the small angle is 360 - 286 = 74 degrees. (I guess it's easier to imagine here that the hands move counterclockwise, but it does not matter.)
Hello, Narek!
What is the small angle between clock hands where it shows 11:08?
The minute hand moves: .
The hour hand moves: .
Using , label the dial from to
At exactly 11 o'clock, the minute hand is at
. . and the hour hand is at
In the next eight minutes:
. . The minute hand has advanced: .
. . The minute hand is at:
. . The hour hand has advanced: .
. . The hour hand is at: .
The angle between the hands is: .