5.5k views
1 vote
What is the number of degrees in the acute angle formed by the hands of a clock at 6:44?

2 Answers

2 votes

Solution:

[asy]

unitsize(0.8inch);

for (int i=0 ; i<=11 ;++i)

{

draw((rotate(i*30)*(0.8,0)) -- (rotate(i*30)*(1,0)));

label(format("%d",i+1),(rotate(60 - i*30)*(0.68,0)));

}

draw(Circle((0,0),1),linewidth(1.1));

draw(rotate(186)*(0.7,0)--(0,0)--(rotate(-22)*(0,-0.5)),linewidth(1.2));

[/asy]

There are 12 hours on a clock, so each hour mark is $360^\circ/12 = 30^\circ$ from its neighbors. At 6:44, the minute hand points at minute 44, which is $\frac45$ of the way from hour 8 to hour 9. Therefore, the minute hand is $\frac45\cdot 30^\circ = 24^\circ$ past hour 8. The hour hand is $\frac{44}{60} = \frac{11}{15}$ of the way from hour 6 to hour 7, so it is $\frac{11}{15}\cdot 30^\circ = 22^\circ$ past hour 6. This means that the hour hand is $30^\circ -22^\circ = 8^\circ$ from hour 7. Since hours 7 and 8 are $30^\circ$ apart, the total angle between the two hands is $8^\circ + 30^\circ + 24^\circ = \boxed{62^\circ}$.

User Paulo Almeida
by
8.3k points
7 votes
The minute hand has moved 44 minutes. Hence, it is at: 44 60 × 360 ∘ = 264 ∘ mark. Hence, the angle between the hands = 264 − 202 = 62
User Velazcod
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories