Find the angle between the hands of a clock at 6:33?

Question

Find the angle between the hands of a clock at 6:33

How would I do this?

Answer 1

The angle that the hour hand makes clockwise from 12:00 is

360 * ( time / 12:00 ) where the times should be expressed in the same units (seconds or minutes)

For this problem,

hour hand angle = 360 * ( ( 6 * 60 + 33 ) / ( 12 * 60 ) )

where the times have been converted into minutes.

The minute hand makes an angle equal to

360 * ( minutes / 60 ).

Find the two angles and take their difference for the angle between them.

Answer 2

The minute hand moves 360 degrees/60 minutes = 6 degrees per minute. Likewise the hour hand moves 1/12 that, so 0.5 degrees per minute. At 6:00, they are precisely 180 degrees apart. As time progresses, the movement of the minute hand decreases the angle, while the hour hand increases it. So, if it is t minutes past 6, this is the angle:

180 - 6t + 0.5t = 180 - 5.5t

At 33 minutes past 6, this is 180 - 5.5*33 = -1.5. One and a half degrees. The negative just means the minute hand has passed the hour hand.

Answer 3

Fine the degrees per minute: 360/60 = 6 degrees per minute
Fine the degrees per hour: 360/12 = 30 degrees per hour
The longer hand on 33 minutes has a larger arc angle.
Longer hand angle from 12:00 - shorter hand from 12:00 ...
6(33) - 6(30)
6(33 - 30)
6 * 3
18 degrees

Answer 4

for each minute:
long hand move 360/60 = 6*
short hand move (360/12)/60 = 0.5*

long hand at 33*6 = 198*
short hand at 180+33*0.5 = 196.5*

answer
= 198 - 196.5
= 1.5°