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The angle between the Minute hand and the Hour hand of a clock when the time is 8:30.

Question

The angle between the Minute hand and the Hour hand of a clock when the time is 8:30.

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Solution 1

Step 1: Calculate the position of the hour hand. At 8 o'clock, the hour hand is at 8*30 = 240 degrees from the 12 o'clock position. However, since it's 8:30, the hour hand is halfway between the 8 and 9. Therefore, it's at 240 + 15 = 255 degrees.

Step 2: Calculate the position of the minute hand. At 30 minutes past the hour, the minute hand is at the 6, which is 180 degrees from the 12 o'clock position.

Step 3: Subtract the smaller angle from the larger angle to find the angle between the two hands. Therefore, the angle between the hour hand and the minute hand at 8:30 is 255 - 180 = 75 degrees.

This problem has been solved

Solution 2

Step 1: Calculate the position of the hour hand. At 8:30, the hour hand is halfway between 8 and 9. Since each hour represents 30 degrees (360 degrees / 12 hours), the hour hand is at 8 * 30 + 15 = 255 degrees.

Step 2: Calculate the position of the minute hand. Each minute represents 6 degrees (360 degrees / 60 minutes), so at 30 minutes, the minute hand is at 30 * 6 = 180 degrees.

Step 3: Calculate the angle between the hour and minute hand. Subtract the smaller angle from the larger angle. So, 255 degrees - 180 degrees = 75 degrees.

Therefore, the angle between the minute hand and the hour hand at 8:30 is 75 degrees.

This problem has been solved

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