CLOCK PROBLEMS: HOW TO GET THE ACUTE/OBTUSE ANGLE FORMED BY A CLOCK AT A CERTAIN TIME?
General Formula:
Angle = |30h - 5.5m|
Where,
h = hours
m = minutes
| | = absolute value
Example 1: Find the angle formed by a clock at 6:09
6 -> hour
9 -> minute
Substitute
Angle = |30h - 5.5m|
Angle = |30(6) - 5.5(9)|
Angle = |180 - 49.5|
Angle = 130.5 degrees (Answer)
Example 2: How about if it is 3:49?
3 -> hour
49 -> minute
Substitute
Angle = |30(3) - 5.5(49)|
Angle = |90 - 269.5|
Angle = |-179.5|
Angle = 179.5 degrees (Answer)
#MMBLTutorial
-shinnichi
From comment section:
1. Every minute, the minute hand moves by 6°. So in x minutes, it will move by an arc of (6x)°.
On the other hand, every hour, the minute hand rotates for 1 whole cycle while the hour hand only moved by 1/12 of an arc of the circle. Hence, every (6x)° sweeps by minute hand the hour hand only moved for (0.5x)° in x minutes.
Let us consider the 12 o'clock mark as the reference point. And every number in the analog clock has a 30° difference. So after h hours, the hour hand sweeps 30h.
The minute hand, sweeps (6m)° every m minutes and (m/2)° for the hour hand after h o'clock. We need to find the angle difference between the hands, so 5.5m.
To remove the unnecessary angles sweep by the hour hand from the 12o'clock mark we need to subtract the two values. That's why, we have the general formula:
angle = |30h - 5.5m|
2. Another example:
What if the time is 11:06?
11 -> hour
6 -> minute
Angle = |30(11) - 5.5(6)|
Angle = |330 - 33|
Angle = |297|
Angle = 297
Since 297° > 180°, subtract the result from 360°
360° - 297° = 63°
