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# help

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

$$\begin{array}{rcll} \Delta\alpha^{\circ} &=& 330 \times t^h \pmod{360^{\circ}} \quad | \quad \mathbf{t^h=6+\dfrac{48}{60} = 6.8\ h } \\ &=& 330 \times 6.8 \pmod{360^{\circ}} \\ &=& 2244^{\circ} \pmod{360^{\circ}} \\ &=& \mathbf{84^{\circ}} \\ \end{array}$$ Nov 20, 2019
#3
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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°   Nov 20, 2019