AMC 8 2003 Problem 20

AMC8 2003 年第 20 题

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What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?

下午 4:20 时，钟面上时针和分针所形成的的锐角是多少度？

A.0
B.5
C.8
D.10
E.12

正确答案 · Correct Answer

解析 · Solution

Solution 1

Imagine the clock as a circle. The minute hand will be at the 4 at 20 minutes past the hour. The central angle formed between 4 and 5 is 30 degrees (since it is

\displaystyle \frac{1}{12}

of a full circle, 360). By

4:20

, the hour hand would have moved

\displaystyle \frac{1}{3}

way from 4 to 5 since

\displaystyle \frac{20}{60}

is reducible to

\displaystyle \frac{1}{3}

. One third of the way from 4 to 5 is one third of 30 degrees, which is 10 degrees past the 4. Recall that the minute hand is at the 4, so the angle between them is 10.

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