What times on a clock form an acute angle.. 2:00 6:40 1:30 12:50?
Which three times do you think form an acute angle?
http://www.mathsisfun.com/acute.html
But, but, ...
my clock has a digital display.
Come on now, just visualize the hands of the clock for the given times, it is quite easy to see.
To determine which times on a clock form an acute angle, we need to find the angle between the hour and minute hands. Here's how you can calculate it:
1. Convert the time on the clock to degrees:
- Each hour mark on a clock represents 30 degrees (360 degrees divided by 12 hours).
- Each minute mark represents 6 degrees (30 degrees divided by 5 minutes for each minute mark).
Let's calculate the angles for each of the given times:
1. For 2:00:
- The hour hand is at the 2-hour mark, which is at 60 degrees (2 * 30).
- The minute hand is at the 12-minute mark, which is at 72 degrees (12 * 6).
- The angle between the hour and minute hands is 72 - 60 = 12 degrees.
2. For 6:40:
- The hour hand is at the 6-hour mark, which is at 180 degrees (6 * 30).
- The minute hand is at the 8-minute mark, which is at 48 degrees (8 * 6).
- The angle between the hour and minute hands is 180 - 48 = 132 degrees.
3. For 1:30:
- The hour hand is between the 1-hour and 2-hour marks, approximately at 45 degrees (1.5 * 30).
- The minute hand is at the 6-minute mark, which is at 36 degrees (6 * 6).
- The angle between the hour and minute hands is 45 - 36 = 9 degrees.
4. For 12:50:
- The hour hand is at the 12-hour mark, which is at 0 degrees (12 * 30).
- The minute hand is at the 10-minute mark, which is at 60 degrees (10 * 6).
- The angle between the hour and minute hands is 60 - 0 = 60 degrees.
Based on the calculations, only the time "1:30" forms an acute angle, which is 9 degrees.