Discussion
A clock shows 3:15. What is the angle between the hour and minute hands ?
Answer: B
The angle is 7.5°.
At 3:15 the minute hand points exactly at 3. The hour hand, though, has moved a quarter of the way from 3 to 4, since a quarter of the hour has passed. One hour on the dial is \(30^\circ\):
\[ \frac{15}{60} \times 30^\circ = 7.5^\circ \]
General formula: angle \(= |30H - 5.5M| = |90 - 82.5| = 7.5^\circ\). 0° is the trap of assuming the hour hand stays on 3; 15° and 22.5° come from using the wrong rate of 1° or 1.5° per minute.
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