What is the measure of the smaller angle between tge hands of analog clock at 10:17
Measuring clockwise from 0 at 12:00,
the hour hand is at 270 + 30 + 30 * 17/60 = 308.5
The minute hand is at 17 * 360/60 = 102
Now, 308.5 is equivalent to -51.5
So the angle is 153.5
To find the measure of the smaller angle between the hands of an analog clock at a given time, you can follow these steps:
1. Understand the clock: An analog clock has three hands - the hour hand, the minute hand, and the second hand. In this case, we are interested in finding the angle between the hour and minute hands.
2. Determine the positions of the hands: At 10:17, the hour hand will be pointing between the 10 and 11 marks, while the minute hand will be pointing at the 17-minute mark.
3. Calculate the angles of the hands: The minute hand makes a complete rotation around the clock in 60 minutes, which is 360 degrees. So, for every minute, it moves 360/60 = 6 degrees. At 17 minutes, the minute hand will have moved 17 * 6 = 102 degrees from the 12:00 position.
The hour hand moves slower than the minute hand. It covers 360 degrees in 12 hours, meaning it moves 360/12 = 30 degrees per hour. But since we are looking at a time within the hour, we need to consider how far the hour hand moves for each minute. In one minute, the hour hand moves 30/60 = 0.5 degrees.
So, at 10:17, the hour hand will have moved 0.5 * 17 = 8.5 degrees from the 10:00 position.
4. Calculate the angle between the hands: To find the angle between the hands, we can subtract the smaller angle from the larger angle. In this case, the minute hand is ahead by 102 degrees, and the hour hand is behind by 8.5 degrees.
Since the minute hand is ahead, and the hour hand is behind, we subtract the smaller angle from the larger angle: 102 - 8.5 = 93.5 degrees.
Therefore, the smaller angle between the hands of the analog clock at 10:17 is 93.5 degrees.