Question

The angle between the minute hand and hour hand of the clock when the time is $05:06$ hours is

• A. ${126}^{\circ }$
• B. ${120}^{\circ }$
• C. ${117}^{\circ }$

Answer 1

The correct option is C ${117}^{\circ }$

To find: Angle between the minute hand and hour hand in a clock when the time is $05:06$ hours.
The sittuation can be represented by a diagram as:

Here, the recquired angle $=\angle COA-\angle BOA$
For hour hand $1$ Rotation $=12$ Hours
And for minute hand $1$ Rotation $=60$ minutes
$\Rightarrow$ Time taken to go from $00:00$ to $05:06$ hours
$=5+\frac{06}{60}=\frac{51}{10}$ hours.
Now, angle traced by hour hand in $12$ hours $={360}^{\circ }$
$\Rightarrow$Angle traced by hour hand in $51/10$ hours $=\frac{51}{10}\times \frac{{360}^{\circ }}{12}={153}^{\circ }=\angle AOC$
Now, for minute hand $1$ Rotation $=60$ minutes
Or angle traced by minute hand in $60$ minutes $={360}^{\circ }$
$\Rightarrow$ Angle traced by minute hand in $06$ minutes $=\frac{{360}^{\circ }}{60}\times 06={36}^{\circ }=\angle AOB$
$\therefore$ Angle made by the minute hand and the hour hand when the time is $05:06$ hours $=\angle AOC-\angle AOB$
$={153}^{\circ }-{36}^{\circ }={117}^{\circ }$