What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at 5:44?

Rudram592 Sep 1, 2019

#1**+3 **

The hour hand will move at a rate of

360° in 12 hrs

30° in 1 hr

30°/ 60 = .5° in one minute

So at 5:44.....the hour hand has moved 5 (30°) + 44(.5°) = [150 + 22]° = 172° from 12 noon

The minute hand will move at a rate of 360°/ 60 = 6° per minute

So at 5:44...it will have moved [44 * 6]° = 264° from the top of the hour

So...the smaller angle formed by the hands = [264 - 172]° = 92°

CPhill Sep 1, 2019

#3**+3 **

**What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at 5:44?**

\(\text{Let the angle formed by the minute hand and hour hand in degrees $\mathbf{ \Delta \alpha }$ } \\ \text{Let the time in hours $\mathbf{ t }$ }\)

The formula between the two values \(\Delta \alpha\) and \(t\) is:

\(\boxed{~ \Delta \alpha = 330 \cdot t } \)

\(\begin{array}{|rcll|} \hline \Delta \alpha &=& 330 \cdot t \quad | \quad t= 5:44 = 5+\dfrac{44}{60}= 5.7\overline{3}\ h \\ &=& 330 \cdot 5.7\overline{3} \\ &=& 1892 \\ &=& 1892 -5\cdot 360 \\ &=& 1892 - 1800 \\ \mathbf{\Delta \alpha} &=& \mathbf{ 92^\circ } \\ \hline \end{array}\)

heureka Sep 2, 2019