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# Clock problem

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What is the number of degrees in the acute angle formed by the hands of a clock at $6:40$?

Dec 28, 2021

#1
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I think it is 40 degrees :-)

Dec 28, 2021
#2
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Hour hand    180 + 40(.5) = 200 degrees

minute hand    40( 6)  = 240 degrees

240 - 200 = 40 degrees

Dec 28, 2021
#3
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6 : 40

Hello Guest!

$${\color{blue}\angle_{6:40}}=40\ min\cdot \frac{360\ degrees}{60\ min}-(6\cdot 60+40)\ min\cdot \frac{360\ degrees}{12\cdot 60\ min}\color{blue}=40\ degrees$$

!

Dec 28, 2021
edited by asinus  Dec 28, 2021