¶ 2025 AMC 12B Problem 16
¶ Problem:
An analog clock starts at midnight and runs for minutes before stopping. What is the tangent of the acute angle between the hour hand and the minute hand when the clock stops?
Answer Choices:
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¶ Solution:
minutes corresponds to hours and minutes, so the analog clock will show .
Hence, the angle between the hour and minute hand is . We can use the half-angle formula to calculate:
so the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions