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Find the smaller angle formed between the hour hand and the minute hand at time 6:48 pm.

 Nov 20, 2019
 #1
avatar+2490 
+1

HINT:

 

Find the angle between the minute hand and 12 o clock.

 

Find the angle between the hour hand and 12 o clock.

 


Find the absolute difference between them.

 Nov 20, 2019
 #2
avatar+23542 
+2

Find the smaller angle formed between the hour hand and the minute hand at time 6:48 pm.

 

\(\begin{array}{rcll} \Delta\alpha^{\circ} &=& 330 \times t^h \pmod{360^{\circ}} \quad | \quad \mathbf{t^h=6+\dfrac{48}{60} = 6.8\ h } \\ &=& 330 \times 6.8 \pmod{360^{\circ}} \\ &=& 2244^{\circ} \pmod{360^{\circ}} \\ &=& \mathbf{84^{\circ}} \\ \end{array} \)

 

 

laugh

 Nov 20, 2019
 #3
avatar+105370 
+1

Here's one more way

 

Call  the top of the clock 0°

Let  6  be located at 180°

 

Every minute....the minute hand moves 6°

Every minute....the hour hand moves  .5°

 

At 6 o'clock.....the hour hand is at 180°  ..and in 48 minutes it moves to 180 + 48(.5) = 180 + 24  = 204°

 

And at 6 0'clock, the minute hand is a 0°.....and in  48 minutes it moves to  48 (6)  = 288° 

 

So....the smaller angle between  them is  288 - 204  =   84°

 

 

cool cool cool

 Nov 20, 2019

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