Angle between the hands at 9:30

Question

Solve in your head. What is the angle between the hour and minute hands at 9:30? Aim: under 15 seconds.

Accepted Answer

At 9:30 the minute hand is at the 6, i.e. 180^\circ from 12. The hour hand is not on the 9, it has drifted halfway from 9 toward 10. Each hour mark spans 30^\circ, and the 9 sits at 270^\circ, so the hour hand is at 270^\circ + 	frac{1}{2}	imes 30^\circ = 285^\circ. Difference: 285^\circ - 180^\circ = 105^\circ. Since 105^\circ < 180^\circ, that is already the smaller angle, so the answer is 105^\circ. Formula check: angle = 30H - 5.5M = 30	imes 9 - 5.5	imes 30 = 270 - 165 = 105^\circ. Same. Takeaway. The minute hand moves 6^\circ per minute and the hour hand 0.5^\circ per minute, so the …

Angle between the hands at 9:30

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