what is the smaller angle between the hour and the minute hand of the clock at 12:20.
120
The angle between the minute hand and the hour hand at 12:20 is 120 degrees.
At 12:20 the minute hand has moved 120° if we consider 12:00 as 0°
Each hour the hour hand moves 30°
At that time of 12:20 the hour hand has moved 20/60 or 1/3 of its 30° movement, so the hour hand has moved 10°
making the angle between the 20 at 12:20 equal to 110°
What is the other angle?
My last sentence makes no sense, it should say
making the angle between the hands at 12:20 equal to 110°
Thanks 4 da answer
To find the smaller angle between the hour and minute hand at 12:20, follow these steps:
Step 1: Calculate the angle formed by the hour hand:
- Divide the total degrees in a circle (360 degrees) by 12 to find the degrees covered by each hour. So, each hour is represented by 30 degrees (360 / 12 = 30).
- Since it's 12:20, the hour hand is pointing directly at 12. To account for the position of the minute hand, we consider the fractional part of the hour. In this case, the hour hand is 1/3 (20 minutes is 1/3 of an hour) of the way between 12 and 1.
- Multiply the fraction of the hour (1/3) by the degrees per hour (30 degrees), which gives us 10 degrees. So, the hour hand is at 12 plus 10 degrees, which is at 120 degrees.
Step 2: Calculate the angle formed by the minute hand:
- Divide the total degrees in a circle (360 degrees) by 60 to find the degrees covered by each minute. So, each minute is represented by 6 degrees (360 / 60 = 6).
- Multiply the minutes (20) by the degrees per minute (6 degrees) to find the position of the minute hand, which gives us 120 degrees.
Step 3: Find the difference between the hour and minute hand angles:
- Take the absolute difference between the hour hand angle (120 degrees) and the minute hand angle (120 degrees) to find the smaller angle.
- In this case, the smaller angle between the hour and minute hand at 12:20 is 0 degrees.