Angle between the hands at 3:15

Question

Solve in your head. What is the angle between the hour and minute hands at 3:15? Aim: under 15 seconds.

Accepted Answer

At 3:15 the minute hand is at the 3, i.e. 90^\circ from 12. The hour hand is not at the 3, it has moved a quarter of the way from 3 toward 4. Each hour mark spans 30^\circ, so it sits at 90^\circ + 	frac{1}{4} 	imes 30^\circ = 97.5^\circ. Difference: 97.5^\circ - 90^\circ = 7.5^\circ. Takeaway. Speeds to memorise: the minute hand moves 6^\circ per minute, the hour hand 0.5^\circ per minute, so the gap closes at 5.5^\circ per minute. General formula: angle = 30H - 5.5M (take the smaller of it and 360^\circ minus it). The trap in every clock question is forgetting the hour hand drifts continu…

Angle between the hands at 3:15

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