give one example of a time after 1:00 and before 2:00 when the hands of the clock form an obtuse angle
Any time after 1:15 because 1:15 forms a right angle(90 degrees) so anything after that(1:16 to 1:59) is an obtuse angle! Hope that helps!! :)
generally true, but the right angle is not at exactly 1:15, because the hour hand has also moved 1/4 of the way from 1 to 2.
after m minutes,
the minute hand has moved m/60*360 = 6m°
the hour hand has moved to 30+m/2°
So, we need to find m when
6m = 30 + m/2 + 90
11m/2 = 120
t = 21.8
So, the hands form a right angle at 1:21:48
After that the angle is obtuse
Well, okay if you want a direct answer, it would be 1:45 or 1:30. Just guessing.
To find an example of a time after 1:00 and before 2:00 when the hands of the clock form an obtuse angle, we need to consider the relative positions of the hour and minute hands.
First, let's understand the layout of the clock. A standard analog clock has 12 hours marked on the circumference, with the hour hand pointing to the hour and the minute hand pointing to the minutes.
To calculate the angle between the hour and the minute hands, we can use the following formula:
angle = |30H - 11M/2|
Where:
H represents the current hour,
M represents the current minute.
Now, let's go step by step to find a time that meets the given condition:
1. Start by considering times between 1:00 and 1:10. At exactly 1:00, the minute hand points at the "12" mark, and the hour hand points halfway between "1" and "2". Therefore, the angle between the hands is an acute angle.
2. Continuing to 1:10, the angle between the hands remains acute.
3. Let's move to 1:20. Here, the minute hand moves further away from the "12" mark, while the hour hand moves closer to the "2" mark. As we calculate the angle, we find that the hands form an obtuse angle. For example, at 1:25, the angle between the hands is approximately 157.5 degrees.
So, one example of a time after 1:00 and before 2:00 when the hands of the clock form an obtuse angle is 1:25.