Angle between clock hands at 3:30

Question

Look at an analog clock at exactly 3:30. What is the angle between the hour hand and the minute hand? A common wrong answer is 90^\circ, make sure you avoid it.

Accepted Answer

Measure everything in degrees from the 12 o'clock position, going clockwise. Minute hand. At 30 minutes it points straight down at the 6. Each minute is 6^\circ (since 360^\circ / 60 = 6^\circ), so the minute hand is at 30 	imes 6 = 180^\circ. Hour hand. The hour hand moves 360^\circ in 12 hours, i.e. 30^\circ per hour, i.e. 0.5^\circ per minute. At 3:30 the time is 3.5 hours past 12, so the hour hand is at 3.5 	imes 30^\circ = 105^\circ. That is, it sits halfway between the 3 (at 90^\circ) and the 4 (at 120^\circ). Angle between them. 180^\circ - 105^\circ = 75^\circ. Takeaway. The clean f…

Angle between clock hands at 3:30

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