What is the angle between the hands of a clock at 9.30?
Answers
This is a pretty good question
Usually people might answer it 90
But a point we miss is that the hour hand is not exactly on 9. It moves and is exactly in between 9and 10
So we have to consider that also..
The req solution is 90+15=105 degrees
Given,
The time on the clock is 9:30
To Find,
The angle between the hands of a clock at a given time.
Solution,
The clock is also a circle and that is why the total degree is 360°
There are 60 minutes in 1 hour and a minute hand covers 360° in 1 hour
Degree covered by minute hand in 1 minute = 360 / 60 = 6 °
Hour hand covers 360 in 12 hours is 12 * 60 = 720 minutes.
Degree covered by hour hand in 1 minute = 360 / 720 = 0.5 °
The minute hand is on 6 and the hour hand is on 9 approximately and
There are 60 minutes between 12 numbers = 60/12 = 5 minutes, that's why,
Minutes between 9 and 6 = 3 * 5 = 15 minutes
hence, Angle between 9 and 6 = 15 * 6 = 90°
But hour hand is not exactly on 9 it is between 9 and 10, therefore, and made by hour hand with 9 = 0.5 * 6 * 5 = 15 °
Total angle = 15° + 90° = 105°
Hence, the angle formed between the hands of a clock at 9.30 is 105°