To find the number of degrees between the clock hands at 3:15 PM, we need to determine the positions of the hour and minute hands.
At 3:00 PM, the hour hand is exactly on the 3, and the minute hand is pointing at the 12.
Between 3:00 PM and 3:15 PM, the hour hand moves a fraction of the way between the 3 and the 4. Since there are 12 hour marks on the clock, the hour hand moves 1/12th of the way between the 3 and the 4.
Between 3:00 PM and 3:15 PM, the minute hand moves to the 3 (15 minutes past the hour).
Therefore, the angle between the minute hand and the hour hand at 3:15 PM is the difference between the positions of the hour and minute hands.
To calculate the angle, we can use the formula:
Angle = |(30 * H) - (11/2 * M)|
Where:
H = Hour hand position
M = Minute hand position
Substituting the values:
H = 3 + 1/12 = 3.0833 (approx.)
M = 15
Angle = |(30 * 3.0833) - (11/2 * 15)|
Angle = |92.4985 - 82.5|
Angle = |9.9985|
Since we need the absolute value of the angle, the answer is approximately 10 degrees.
Therefore, the correct answer is Option E) 7.5.