How many degrees are in the smaller angle formed by the minute and hour hands on a clock at 12:30?
the hr hand is 1/12 of the way from 12 to 6
... the min hand is on 6
... 11/12 * 180º
IN ALL ... climb + slide + walk
57 + √(57^2 + 76^2) + 76
To determine the number of degrees in the smaller angle formed by the minute and hour hands on a clock, we need to calculate the angle between them. Here's how to do it:
1. Start by determining the position of the hour hand. Since it is 12:30, the hour hand is halfway between the 12 and the 1. In other words, it has moved half the distance between the two hour marks.
2. Each hour mark is 30 degrees apart, so moving halfway between the 12 and the 1 means that the hour hand has covered 30/2 = 15 degrees.
3. The minute hand points directly at the 6, which is in line with the 12. Therefore, the minute hand covers a full 360 degrees each hour. Since it is 30 minutes past the hour (12:30), the minute hand has covered 30 degrees (30 minutes / 60 minutes per hour * 360 degrees per hour).
4. To find the angle between the two hands, we subtract the smaller angle from the larger angle. In this case, the smaller angle is 15 degrees (hour hand) and the larger angle is 30 degrees (minute hand).
5. By subtracting 15 degrees from 30 degrees, we get 30 - 15 = 15 degrees.
So, the smaller angle formed by the minute and hour hands on a clock at 12:30 is 15 degrees.