The smaller angle between the hands of a clock at 8:43 is what?
Spirit of Math, huh you meme
hour hand : 8:43 = (8 + 43/60)/12
= 523/720 around the face of the clock
if we let 12:00 be 0°, then the hour hand
forms an angle of 523/720 * 360 = 261.5 °
the minute hand forms and angle of 43/60*360 = 258°
so the angle between the hands is 3.5°
check my arithmetic
Well, at 8:43, the smaller angle between the hands of a clock is like trying to find parking in a crowded circus: pretty tricky! The minute hand is pointing at the 9 and the hour hand is somewhere between the 8 and the 9. So, be prepared for a wild ride because the smaller angle is about to clown around and make things confusing. To calculate the angle, we need to determine the positions of the clock hands more precisely. Bear with me while I put on my clown hat, hop on my unicycle, whip out my calculator, and get back to you with the answer! 🤡
To find the smaller angle between the hands of a clock at a specific time, you can follow these steps:
Step 1: Convert the given time into an angle measure.
- Each hour mark on a clock represents 30 degrees (360 degrees ÷ 12 hours).
- Each minute mark represents 6 degrees (360 degrees ÷ 60 minutes).
- Here, the hour hand is at 8, which means it has moved 8 hours past the 12 o'clock mark.
- The minute hand is at 43, which means it has moved 43 minutes past the hour.
Step 2: Calculate the position of each hand on the clock.
- The position of the hour hand is given by: (hour * hour mark value) + (minutes * hour mark value ÷ 60)
- The position of the minute hand is given by: minutes * minute mark value
Step 3: Calculate the angle between the hands.
- Find the difference between the positions of the hour and minute hands.
- Take the absolute value of this difference to ensure we get a positive angle.
Now, let's calculate the angle between the hands at 8:43:
Step 1: Convert the time to angles:
- The hour hand is at 8, so its position is (8 * 30 degrees) + (43 * 30 degrees ÷ 60) = 240 + 21.5 = 261.5 degrees.
- The minute hand is at 43, so its position is 43 * 6 degrees = 258 degrees.
Step 2: Calculate the angle difference:
- The angle between the hands is the absolute difference between the positions of the hour and minute hands: |261.5 - 258| = 3.5 degrees.
Therefore, the smaller angle between the hands of a clock at 8:43 is 3.5 degrees.