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What is the angle between two clock hands at 5:51?

 May 29, 2020
 #1
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H=5; M=51; A=abs((30*H) - (5.5*M));print"A =", A,"Degrees")

 

A = 130.5 Degrees [This is the smaller angle].

 May 29, 2020
 #2
avatar+10084 
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What is the angle between two clock hands at 5:51?

 

Hello Guest!

 

\(\omega_{small} =2\pi/12h\\ \alpha_{small}=t\cdot \omega_{small}=(5+\frac{51}{60})h\cdot\frac{\pi}{6h}\)

\(\alpha_{small}=\frac{5+\frac{51}{60}}{6}\pi\)

\(\alpha_{small}=0.975\pi\)

 

\(\omega_{large} =2\pi/60min\\ \alpha_{large}=51min\cdot \frac{\pi}{30min}\)

\(\alpha_{large}=1.7\pi\)

 

\(\Delta\alpha=(1.7-0.975)\cdot\pi\\ \Delta\alpha=0.725\cdot\pi\cdot \frac{180\ deg}{\pi}\)

\(\Delta\alpha=130.5\ deg\)

The angle between two clock hands at 5:51 is 130.5 degrees.

laugh  !

 May 29, 2020
edited by asinus  May 29, 2020
 #3
avatar+26767 
+1

Hour hand starts at 5 *30 = 150 o    moves 1/2  degree per minute     150 + 1/2 x 51 = 175.50

minute hand moves 6o per min     6 x 51 = 306o

306 - 175.5 = 130.5o

 May 30, 2020

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