How many times does the hour and minute hands make an angle of 30 degrees with each other in a clock? Determine the times.
Somebody please explain this question.
Answers
Answer:
The minute hand and hour hand will be separated by 30 degrees twice every hour. Approaching, and leaving the hour hand. So, 48 times in 24 hours
Given: The hour and minute hands make an angle of 30 degrees with each other in a clock.
To find: The number of times the hour and minute hands make an angle of 30 degrees with each other in a clock.
Solution:
A clock is divided into 12 parts and is usually a circle which is 360°. So each part is measured to be 30°. Also, each part represents 1 hour by the hour hand and 5 minutes by the minute hand on the clock.
The hour hand and the minute hand make an angle of 30° once in an hour. Thus, they make an angle of 30° with one another 12 times in 12 hours and 24 times in a day.
The angle made by the two hands the other way round is not considered because when the minute hand is left behind the hour hand, the angle between them would be 330° (360° - 30°), not 30°.
Therefore, the number of times the hour and minute hands make an angle of 30 degrees with each other in a clock is once in an hour or 24 times a day.