Angle Traced by the Hour Hand of a Clock

When we talk about the angle traced by the hour hand of a clock, we are referring to the angle between the hour hand and the 12 o'clock position. This angle is measured in degrees and represents the amount of rotation that the hour hand has made around the clock face.

Calculating the Angle Traced by the Hour Hand

To calculate the angle traced by the hour hand of a clock between two given times, we need to follow these steps:

1. Calculate the number of hours between the two times.
2. Convert the number of hours into degrees.
3. Calculate the additional degrees added by the hour hand due to the minutes that have elapsed.

Calculating the Number of Hours Between 5:15 AM and 5:45 PM

To calculate the number of hours between 5:15 AM and 5:45 PM, we need to subtract the earlier time from the later time:

5:45 PM - 5:15 AM = 12 hours and 30 minutes

Since we only need the number of hours, we can round this down to 12 hours.

Converting the Number of Hours into Degrees

There are 360 degrees in a full rotation around the clock face, and there are 12 hours on a clock face. Therefore, each hour represents 30 degrees:

360 degrees / 12 hours = 30 degrees per hour

Since we have 12 hours between 5:15 AM and 5:45 PM, we can multiply 12 by 30 to get:

12 hours x 30 degrees per hour = 360 degrees

Calculating the Additional Degrees Added by the Hour Hand Due to Minutes

The hour hand moves at a rate of 0.5 degrees per minute. Therefore, we need to calculate the additional degrees added by the hour hand due to the 30 minutes that have elapsed between 5:15 AM and 5:45 PM:

0.5 degrees per minute x 30 minutes = 15 degrees

Calculating the Total Angle Traced by the Hour Hand

To calculate the total angle traced by the hour hand of a clock between 5:15 AM and 5:45 PM, we need to add the degrees from step 2 and step 3:

360 degrees + 15 degrees = 375 degrees

Therefore, the angle traced by the hour hand of a clock between 5:15 AM and 5:45 PM is 375 degrees.