Tag: creativity

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.

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