What is the smaller angle between the minute and hour hands at 12:46 AM? Â

To do: Find the smaller angle between the minute and hour hand at 12:46 AM

Solution:

In 12 hours the hour hand will complete 360 degree. In 12: 46 min it will turn by

$\frac{12 + \frac{46}{60}}{12}  \times  360 = 383*$

In 1 hour , the minute hand will turn by 360 degree, in 46 min it will turn by 

$\frac{46}{60} \times360 = 276*$

The difference between them is $383 - 276 = 107$

At 12:46 AM the smaller angle between the minute and hour hands is 107* 

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Updated on: 10-Oct-2022

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