钟表夹角 II

3:15 时分针指向 3。

时针在第 3 个小时内走了 15 分钟，即从 3 到 4 的 $1/4$ 距离。相邻数字间夹角 30 度，因此夹角为

$$\frac{1}{4}\cdot 30^{\circ}=7.5^{\circ}.$$

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Original Explanation

We know that both hands will be very close to each other but should note that the hour hand will be slightly further clockwise than the minute hand because it's been $15$ minutes into the $3^{\text{rd}}$ hour. In fact, it is precisely one-fourth of the way between the $3$ and $4$. Since there are $12$ total spaces between numbers of the clock, each space has to occupy $30^{\circ}$. Thus, $\frac{1}{4} \cdot 30^{\circ} = 7.5^{\circ}$.