The larger angle between the hands of a clock at 10:30am. is
75 degrees.
To find the angle between the hands of a clock at a specific time, we use the following formula:
Angle = |(30H - 11/2M)|
where H is the hour (in 12-hour format) and M is the minute.
For 10:30am, H = 10 and M = 30. Plugging these values into the formula, we get:
Angle = |(30 x 10 - 11/2 x 30)|
= |(300 - 165)|
= 135 or 225 degrees
However, we need to take into account that the minute hand is only halfway between the 10 and 11 on the clock face. This means that the hour hand has moved a little past the 10 o'clock mark, creating a smaller angle between the hands.
To find this smaller angle, we need to subtract the angle covered by the hour hand from the total angle calculated above. The hour hand moves 30 degrees for every hour, or 0.5 degrees for every minute. At 10:30am, the hour hand has covered:
0.5 x (10 x 60 + 30) = 0.5 x 630 = 315 degrees
Subtracting this from the total angle, we get:
Angle = 225 - 315 = -90
This is a negative angle, which means that we have gone past the 12 o'clock mark and need to add 360 degrees to get the positive value:
Angle = -90 + 360 = 270 degrees
Therefore, the larger angle between the hands of a clock at 10:30am is 270 degrees.
To determine the larger angle between the hands of a clock at 10:30 am, we need to calculate the angle between the hour and minute hands.
First, let's calculate the angle made by the hour hand at 10:30 am.
Since the hour hand moves 360 degrees in 12 hours, we can calculate how far it has moved from the 12 o'clock position at 10:30 am.
10:30 am is half an hour past 10 o'clock, meaning the hour hand has moved 1/2 of the distance between 10 and 11 o'clock.
The angle covered by the hour hand in 1 hour is 360/12 = 30 degrees.
Therefore, the hour hand has moved 1/2 * 30 degrees = 15 degrees.
Now, let's calculate the angle made by the minute hand at 10:30 am.
The minute hand moves 360 degrees in 60 minutes, so in 30 minutes, it moves 30/60 * 360 degrees = 180 degrees.
Next, we calculate the difference between the angles made by the hour and minute hands.
The larger angle is obtained by taking the maximum difference between the two angles:
180 degrees (angle made by the minute hand) - 15 degrees (angle made by the hour hand) = 165 degrees.
Therefore, the larger angle between the hands of a clock at 10:30 am is 165 degrees.