The angle between the hands at 3:15

Question

At 3:15 the minute hand points exactly at the 3. What is the angle between the hour hand and the minute hand? The tempting answer is zero. Explain where the hour hand actually is, and give the general formula for the angle at any time H:M.

Accepted Answer

Seven and a half degrees. The hour hand moves. In 60 minutes the hour hand travels from one numeral to the next, 30 degrees. In 15 minutes it travels a quarter of that: 7.5 degrees past the 3. The minute hand. At 15 minutes past, it points exactly at the 3, that is, 90 degrees clockwise from the 12. The angle. The hour hand is at 90 + 7.5 = 97.5 degrees and the minute hand at 90 degrees. The angle between them is 7.5 degrees. The formula. For time H:M, the angle between the hands is 30H minus 5.5M degrees (take the smaller of that and 360 minus that). For 3:15: 90 minus 82.5 = 7.5. The same f…

The angle between the hands at 3:15

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