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What is the measure, in degrees, of the acute angle formed by the hour hand and the minute hand of a 12-hour clock at 6:48?

 Jan 29, 2019
 #1
avatar+6187 
+3

\(\text{let's use the navigational assignment of degrees to the clock, i.e. }\\ \text{12 is 0 degrees increasing as we move clockwise back to 360 degrees again at 12}\\ \phi_m = 360\dfrac{min}{60} = 360\dfrac{48}{60} = 360 \dfrac 4 5 = 72\cdot 4 = 288^\circ\\ \phi_h = 360 \dfrac{60hr + min}{720} = 360 \dfrac{60\cdot 6 + 48}{720} = \dfrac 1 2(360+48) = 204^\circ\\ |288^\circ - 204^\circ| = 84^\circ\)

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 Jan 29, 2019
 #2
avatar+1116 
0

You can use the clock angle formula, which is \(|0.5\times (60\times H-11\times M)|\), where H is the number of hours and M is the number of minutes.

 

\(|0.5\times (60\times 6-11\times 48)| = |0.5\times (360-528)| = |0.5\times (-168)|=|-84|=84\)

Therefore, the angle between the hands is 84 degrees.

 

You are very welcome!

:P

 Jan 29, 2019
 #3
avatar+4569 
+3

The shortened version of the formula is: \(|30H-5.5M|\), where \(H\) stands for hours and \(M\) stands for minutes. Thus, we have \(|30(6)-5.5(48)|=|180-264|=\boxed{84}\) degrees.

 Jan 29, 2019
 #4
avatar+111328 
+1

Thanks tertre.....I'm going to have to remember that formula!!!!

 

 

cool cool cool

CPhill  Jan 29, 2019
 #5
avatar+4569 
+2

Yes, it's pretty neat!

tertre  Jan 30, 2019

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