The angle between the hour hand and the minut | vedclass

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Question

(B) The position of the hour hand is determined by the total time passed since $12:00$. At $4:55$,the time passed is $4$ hours and $55$ minutes,which

Vedclass · Accepted Answer

$182 \frac{1}{2}$

Vedclass · Answer

(B) The position of the hour hand is determined by the total time passed since $12:00$. At $4:55$,the time passed is $4$ hours and $55$ minutes,which is $4 + \frac{55}{60} = 4 + \frac{11}{12} = \frac{59}{12}$ hours.The hour hand moves $360^{\circ}$ in $12$ hours,so it moves $30^{\circ}$ per hour.Angle traced by the hour hand $= \frac{59}{12} 	imes 30^{\circ} = \frac{59 	imes 5}{2} = \frac{295}{2} = 147.5^{\circ}$.The minute hand moves $360^{\circ}$ in $60$ minutes,so it moves $6^{\circ}$ per minute.Angle traced by the minute hand $= 55 	imes 6^{\circ} = 330^{\circ}$.The angle between the two hands $= |330^{\circ} - 147.5^{\circ}| = 182.5^{\circ}$ or $182 \frac{1}{2}^{\circ}$.

The angle between the hour hand and the minute hand of a clock when the time is $4:55$ is (in $^{\circ}$)

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