At 3:40, what angle do the hands make?
A normal-level "Angle" problem.Six degrees a minute for the minute hand, half a degree for the hour hand. Those two numbers solve every clock-angle problem the same way.
Hints
- You cannot get the angle between the hands directly. Instead, take 12 o'clock as 0° and work out how far each hand has turned, then subtract.
- The minute hand goes 360° in 60 minutes, so 360 ÷ 60 = 6° per minute. In 40 minutes it has turned 40 × 6 = 240°.
- The hour hand goes round once in 12 hours, so 360 ÷ 12 = 30° per hour. At exactly 3 o'clock it would be 3 × 30 = 90°.
- But it is 3:40, so the hour hand has crept a little past the 3 mark. Forgetting this is the classic mistake here.
- The hour hand covers 30° in 60 minutes, i.e. 30 ÷ 60 = 0.5° per minute. In 40 minutes that is 40 × 0.5 = 20°. Total: 90 + 20 = 110°.
- Both turns from 12 are now known. Subtract the smaller from the larger to get the angle between the hands. 240 − 110
Answer 130°
More "Angle" problems
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