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钟表夹角 I

Clock Angle I

专题
Brainteaser / 脑筋急转弯
难度
L2

题目详情

求传统钟表在晚上 9:45 时，分针与时针的夹角（单位：度）。

Determine the angle (in degrees) formed between the minute and hour hands at 9:459:45 PM on a conventional clock.

解析

9:45 时分针指向 9。

时针从 9 向 10 走了 3/43/4 个刻度。相邻数字间夹角为 360/12=30360/12=30 度，因此夹角为

34⋅30=22.5∘.\frac{3}{4}\cdot 30=22.5^{\circ}.

Original Explanation

At 9:459:45 PM, it's clear that the minute hand points to the 99. The hour hand is positioned at 34\frac{3}{4} of the distance between the 99 and the 1010, since 34\frac{3}{4} of an hour has passed. Consequently, the angle formed between the two hands is simply 34\frac{3}{4} of the angular distance from 99 to 1010 on the clock face. Specifically, with 1212 evenly spaced numerical values and a total circle measurement of 360360 degrees, there are 3030 degrees between each numerical marker. Thus, our result is 34⋅30=22.5\frac{3}{4} \cdot 30 = 22.5.