Final answer:
The smaller angle between the hands of a clock at 8:43 is calculated as the difference in degrees between the positions of the hour and minute hands. The hour hand is at 261.5 degrees, the minute hand at 258 degrees, resulting in a 3.5-degree angle between them.
Step-by-step explanation:
To find the smaller angle between the hands of a clock at 8:43, we need to calculate the positions of the hour and the minute hands at that time. Each hour represents 30 degrees on the clock (360 degrees / 12 hours), and each minute represents 6 degrees (360 degrees / 60 minutes).
At 8:43, the hour hand is between the 8 and the 9. Since 43 minutes past the hour have passed, the hour hand has moved 43 minutes out of 60 of the way from 8 to 9, which represents 43/60 of 30 degrees. So, the hour hand is at 8 hours times 30 degrees per hour plus (43/60) times 30 degrees, totaling 240 + 21.5 = 261.5 degrees from the 12 o'clock position.
The minute hand at 43 minutes is at 43 times 6 degrees, equaling 258 degrees from the 12 o'clock position. To find the angle between the two, we take the smaller difference: |261.5 degrees - 258 degrees|, which equals 3.5 degrees.
Therefore, the smaller angle between the hands of a clock at 8:43 is 3.5 degrees.