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

Guest Nov 20, 2019

#1**+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.

CalculatorUser Nov 20, 2019

#2**+2 **

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

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

heureka Nov 20, 2019

#3**+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°

CPhill Nov 20, 2019