Question

Find the angle between the minute hand of a clock and the hour hand when the time $7:20$ AM.

Answer 1

We know that the hour hand completes one rotation in 12 hours while the minute hand completes one rotation in 60 minutes.

$\therefore$ Angle traced by the hour hand in 12 hours $={360}^{\circ }$

$\Rightarrow$ Angle traced by the hours hand in 7 hrs 20 mini.e., $\frac{22}{3}hrs={(\frac{360}{12}\times \frac{22}{3})}^{\circ }={220}^{\circ }$

Also, the angle traced by the minute hand in 60 min $={360}^{\circ }$

$\Rightarrow$ The angle traced by the minute hand in 20 min $={(\frac{360}{60}\times 20)}^{\circ }={120}^{\circ }$

Hence, the required angle between two hands $={220}^{\circ }-{120}^{\circ }={100}^{\circ }$