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The angle between hours and minutes for a given time x:y(x hours and y minutes) is |30*x-11*y/2|(absolute value)..this comes from the fact that a hour hand elapses 30 degrees for every hour(360/12) and minute hand elapses 6 degrees(360/60)..but for 6:50,the hour hand also elapses extra offset from its original position where it has to be there at 6:00 sharp..the offset is calculated as follows:
1.for every 60 minutes of minutes hand,hour hand elapses 1 hour..so distance travelled by hour hand when the minute hand travels 1 min is 1/60
2.so the offset is (50/60)*30 degrees for the hour hand
3.so the total angle covered by hour hand for 6:50 is 6*30 degrees+offset=180+25=205 degrees
4.angle covered by minute hand is 50*6 degrees=300 degrees
So,angle between them =300-205=95 degrees :)

(11/2) * M - (30) * H
Here M is minute and H is hour.
ANS= 95 degree.

Angle in Degree=(abs(1/2*(60*Hours+minutes) - (6*minutes))

More details refer :
//en.wikipedia.org/wiki/Clock_angle_problem

95 degrees

how??

95! duh

Angle = (h*30 + (m/60) * 30) - (m * 6)

For hour hand,
1 hour = (360/12) = 30 degrees movement
1 minute = (30/60) = 0.5 degree movement

For minute hand,
1 minute = (360/60) = 6 degrees movement

So, if time is H:M
Angle between two hands = |((30*H)+(0.5*M))-(6*M)|

6:50 will give 95 degrees

Hey guys. My math skills suck but please explain why wouldn't it be 120°, since it's the only answwer I coud actually explain to my interviewer.

formula: 30H-(11/2)M

angle b/w the hands of watch=|(11 m-60 h)/2|

- At 6:50, the minute hand is sitting on 10 and the hour hand is just shy of sitting on the 6.

- There are 12 hours in 360*, so one hour = 360/12 = 30 deg

- The angle between 6 and 10 = (10 -6) * 30 = 120 deg

- The hour hand is 10/12 of the way from the 5 to the 6:

30 * 10 / 12 = 25 deg

So the hour hand is 30 - 25 = 5 deg away from the 6.

- Total angle between hour & minute hand = 120 + 5 = 125 deg

I also got 95 degrees. Here's how.

Suppose the hour and minute hands were pointing to 6:00, then there's a 180 degree angle since it's a straight line.

Now, return to the time of 6:50. The minute hand sits on the 10. For each increase in number, there is a 360/12 = 30 degree rotation. So the angle between the 12 and 10 is 2*30 = 60 degrees.

Now consider the angle between the hour hands at 6:00 and 6:50. This is 5/6 of an hour, or 5/6 of a number change. Thus, the angle is 30*(5/6) = 5*5 = 25 degrees.

Since 12:00 and 6:00 make a straight line (180 degrees), we have

60 + x + 25 = 180
x = 180 - 60 - 25
x = 95

Kind of a long response. But easy to explain.

Obtuse angle

/* This is program to find the angle between Hour Hand and Minute Hand*/

#include<stdio.h>
#include<math.h>
int main()
{
int hour = 2;// totally 360 degrees ,12 hours(760 Minutes) = 360 degress, 1 minute = 0.5 degress
int minute =20;// totally 360 degrees ,60 minutes = 360 degress, 1 minute = 6 degress
int degree = 0;
hour = (hour*60+minute)/2;
minute=(minute*6);
printf(" The angle betwenn hour and minute hand is %d\n",hour-minute);
return 0;
}

Worth noticing there is an article about this problem at wikipedia:Clock_angle_problem

osm

Answer should be 95 degress.

A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute.


Angle b/w hour and minute hand is => ½ *(total minutes) - 6 * minutes
for 6:50 then angle will be
½*(6*60 + 50) - 50*6 => ½ * (410) - 3000 => 205-300 => 95 degrees

In 12 hours, the hands of a clock are at right angles 11 times to the left of the number 12, and 11 times to the right of the number 12 – that is, 22 times
Therefore, in 24 hours, they are at right angles 44 times.

I'm reading Cracking the coding interview and she suggests the answer is (30h - 5.5m) % 360 but I did not understand how she got that and I tried some tests and maybe i'm mistaken but it doesn't seem to work.

My thinking was that if you consider noon to be 0 and you first look for the angle of the hour hand from 0 and get that number and then do the same thing for the minute hand and then subtract the two you would get your answer (ofcourse checking if the angle was greater than 180 and if so subtracting by 360 to get the smaller angle).

So at 1 PM, the hour hand is at 1 and the angle from noon is 360/12 = 30.
And at 12:01 pm, the minute hand is at 1 minute and the angle from noon for the minute hand is 360/60 = 6.

can someone tell me if this is the right or wrong answer?

static int GetAngle(int h, int m)
	{
		int hAngle = 30 * (h % 12);
		int mAngle = 6*m;
		int diff = Math.Abs(hAngle-mAngle);
		if (diff > 180)
		{
			diff = 360 - diff;
		}
		return diff;
	}

Also do not forget the 24 hour system

public class Angle {
	public static void main(String args[]){
		float hr=12;  //time hour
		float min=5;  //time minute 
		if (hr>=12){
			hr-=12;
		}
		float ang=360/60;         //Unit Angle 
		float mv=(float)5/60;     //Hour hand movement per minute
		float hr1=hr*5+mv*min;    //Hour hand position
		System.out.println("hr1: "+hr1);
		if(hr1>min){
			float temp=hr1-min;
			System.out.println("Angle="+temp*ang);
		}
		else{
			float temp=min-hr1;
			System.out.println("Angle="+temp*ang);
		}
	}

264 degree / 96 degree..

for acute angle:
(11/2) * M - (30) * H = angle/answer
M=minute
H=hour

for reflex angle:
(11/2) * M - (30) * H = answer
answer + 360 = angle/answer

ref: saumya

nice explanation..thank u

9.9

Angle between hour hand and minut hand at 7:19

Areeb@16

i luv u

The answer is 92.72 Degrees to be accurate all other methods are just rough ones!!!!

12:30

What will be the angle at 7:38?

Nice explanation dude.....

95

30H-(11/2)×min
Eg. Time is 12:20
Then,
Angle = 30 ×(H) - (11/2) ×min
=30×12 - 11/2) ×20
=360 -110
=250 degree

What is the angle between 9to 9:35

1:30

Hour hand angle for a hour= 360/12=30deg
Hour hand angle for a min=360/(12*60)=0.5deg
Min hand angle for a minute= 360/60=6 deg
Hour hand moves 30 deg for an hour and 0.5 deg for min
Minute hand moves 6 deg for min
Hour hand angle = (6*30)+(0.5*50)=205deg
Minute hand angle=(50*6)=300deg
Angle between= 300-205=95deg

what is the angle between 3hours to 12minute

Formula for finding clock angle= |(30*hour + min/2) - (6*min)|
Since the answer should always be in positive.

Formula for finding clock angle= |30*hour + min/2 - (6*min)|
The answer should always be in positive.

this is an equation I made to solve angles,
(|60*h-11*m|)/2
h is the hour
m is the min
| means absolute value

Find the time between 5 or 6 when the angle is 60 degree

2:10:15 par braht angel

Use this formula
1/2(60H-11M) for degree
Note:- If there is negative answer in bracket remove negative answer
For Example 3 hour 15min
1/2(60x3-11x15)
=1/2(180-165)
=1/2x15
=7.5 degree.

How to prove 1 degree is equal to 60 minutes? By calculative method