show tha minute hand of a clock gains 5 degree 30 minutes over the hour hand in one minute?
In one minute the minute hand advances 1/60 of a circle, or 6 degrees.
In that same time, the hour hand advances 1/12 as much, or 30 minutes.
subtract to get the result.
To show that the minute hand of a clock gains 5 degrees and 30 minutes over the hour hand in one minute, we need to take the following steps:
Step 1: Calculate the angles covered by the hour and minute hands in one minute.
The hour hand moves 30 degrees in 60 minutes (360 degrees divided by 12 hours).
Therefore, the hour hand moves 30 degrees in 60 minutes divided by 60 (converting minutes to hours) which equals 0.5 degrees per minute.
The minute hand moves 360 degrees in 60 minutes, which equals 6 degrees per minute.
Step 2: Find the difference in angles covered by the minute and hour hands in one minute.
Since the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute, the difference in their angles covered is:
6 degrees (minute hand) - 0.5 degrees (hour hand) = 5.5 degrees.
Step 3: Convert the difference to degrees and minutes.
To convert 5.5 degrees to degrees and minutes, we need to recognize that 1 degree is equal to 60 minutes and divide the difference by this value.
5.5 degrees / 1 degree = 5 degrees and 30 minutes.
Therefore, the minute hand of a clock gains 5 degrees and 30 minutes over the hour hand in one minute.