What is the angle between the hour and minute hands of a clock at 6:05?
I have tried this
Hour Hand:
12 hour = 360°
1 hr = 30°
Total Hour above the Clock is $\frac{73}2$ hours
In Minute Hand:
1 Hour = 360°
1 minutes = 6°
Total Minutes covered by $6\times 5= 30$
$\frac{73}{2} \cdot30-30=345^\circ$ Is it Correct?
Best Answer
Think of it this way: five minutes after six, the minute hand is $\frac1{12}$ of the circle ahead from 12, while the hour hand has advanced $\frac1{12}$ of the way towards 7 from 6, or $\frac1{144}$ of the circle ahead. The initial angle between the two hands is $\frac12$ of the circle, so the solution is $$\frac12-\frac1{12}+\frac1{144}=\frac{61}{144}=152.5^\circ$$