What is the measure, in degrees, of the acute angle formed by the hour hand and the minute hand of a 12-hour clock at 6:48?
We know that at 6:00 they are 180 degrees from each other. Every minute, the hour hand moves 1/2 of a degree, and the minute hand moves 6 degrees. So in 48 minutes, the hour hand moves 24 degrees and the minute hand moves 288 degrees. 288-180-24=84. So, 84 degrees.
that was wrong
Thank you @yy.julie!! I was having problems with this
To find the measure of the acute angle formed by the hour hand and the minute hand at a given time on a 12-hour clock, you can use the following steps:
1. Calculate the angle formed by the hour hand:
- Divide the hours on the clock (12) into 360 degrees, giving you 30 degrees per hour.
- Multiply the number of hours (6) by the degree value per hour (30), resulting in 180 degrees.
- Note that at 6:00, the hour hand points directly at the 6.
2. Calculate the angle formed by the minute hand:
- Divide the minutes on the clock (60) into 360 degrees, giving you 6 degrees per minute.
- Multiply the number of minutes (48) by the degree value per minute (6), resulting in 288 degrees.
- Note that at 48 minutes past the hour, the minute hand will be 288 degrees ahead of the 12.
3. Calculate the angle between the hour hand and the minute hand:
- Subtract the angle formed by the hour hand (180 degrees) from the angle formed by the minute hand (288 degrees).
- The result is 108 degrees, which represents the angle between the hour hand and the minute hand at 6:48 on a 12-hour clock.
Therefore, the measure of the acute angle formed by the hour hand and the minute hand of a 12-hour clock at 6:48 is 108 degrees.
angle of hour hand: each 12 hours, it goes 360 deg
Angle hour hand= 360*(6 48/60)/12
Angle minute hand: each hour it goes 360 det
Angle Minute Hand: 360*(48/60)
now subtract one angle from the other, that is the difference in angles.