Find the measure of the angle formed by the hands of a clock at 9:43.
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To find the measure of the angle formed by the hands of a clock at a given time, we need to understand a few key concepts:
1. A clock is divided into 12 equal parts, representing the hours.
2. In a clock, the hour hand completes a full revolution in 12 hours.
3. In a clock, the minute hand completes a full revolution in 60 minutes.
Now, let's find the measure of the angle formed by the hands of a clock at 9:43.
1. Calculate the position of the hour hand:
- At 9:00, the hour hand points directly at the 9, which is 3/4 of the way between the 9 and the 10 (counterclockwise).
- From 9:00 to 9:43, the hour hand moves an additional (43/60) * (1/12) of the distance between the 9 and the 10.
- Multiply (43/60) by the fraction (1/12), then add it to 3/4. This will give us the position of the hour hand.
2. Calculate the position of the minute hand:
- At 9:43, the minute hand points directly at the 43 (counterclockwise).
- To find the position of the minute hand, divide 43 by 60 and multiply the result by 360 degrees.
3. Calculate the angle between the hour hand and the minute hand:
- Subtract the position of the hour hand from the position of the minute hand.
- If the difference is negative, add 360 degrees to it.
Calculating these steps, we find the measure of the angle formed by the hands of the clock at 9:43 to be approximately 37.50 degrees.