Favorite Math Problem
Find the measure of the smaller angle between the hands of a clock at 8:16am ( Note: In degrees not radians )
Hint One - minute hand
*notice how many minutes are in one hour and how many minutes are being used
Since there is 16 minutes being used in one hour we can say = 16/60 minutes per hour
Also, there is 360 degrees in a circle and our clock can be represented as a unit circle.
So,
16/60 multiplied by 360 degrees = 96 degrees
Therefore, our minute hand of 16/60 is represented at 96 degrees.
*notice how many minutes are in one hour and how many minutes are being used
Since there is 16 minutes being used in one hour we can say = 16/60 minutes per hour
Also, there is 360 degrees in a circle and our clock can be represented as a unit circle.
So,
16/60 multiplied by 360 degrees = 96 degrees
Therefore, our minute hand of 16/60 is represented at 96 degrees.
Hint Two- hour hand
*notice the hour between 8 and 9 o’clock and how many minutes have gone by
Since the hour hand is 16 minutes past 8 o’clock we can say = 16/60 minutes per hour
Since there is 12 hours shown on the clock,
between 8 and 9 o’clock can be represented as 1/12.
Also, there is 360 degrees in a circle and our clock can be represented as a unit circle.
So,
16/60 multiplied by 1/12 multiplied by 360 degrees = 8 degrees
Therefore, our hour hand is 8 degrees past 8 o’clock..
Hint Three- hour hand
* 12 to 3 am, 3 to 6 am, 6 to 9 am, 9 to 12 am represent 90 degree angles.
Since, 16/60 multiplied by 1/12 multiplied by 360 degrees = 8 degrees
Therefore, our hour hand is 8 degrees past 8 o’clock..
6 o’clock to 9 o’clock forms a right angle. 6 to 7, 7 to 8, and 8 to 9 would be an equal 30 degrees.
If before the hour hand to 8 o’clock is 8 degrees, then after the hour hand to 9 o’clock is 22 degrees.