Question
Find the angle between hour-hand and minute-hand in a clock at : thirty five past one
✓
Answer
At $1 : 35$ the minute -hand is at mark $7$ and hour -hand has crossed $(\frac{7}{12})$th of angle between $1$ and $2.$
Angle between two consecutive marks
$=360^{\circ} / 12=30^{\circ}$
Angle traced by hour-hand in 35 minutes
$=\frac{7}{12}\left(30^{\circ}\right)=\left(\frac{35}{2}\right)^{\circ}=\left(17 \frac{1}{2}\right)^{\circ} \frac{1}{3}$
Angle between marks 1 and $7=6 \times 30^{\circ}=180^{\circ}$
Angle between two hands of the clock at thirty five
$ \text { past one }=180^{\circ}-\left(17 \frac{1}{2}\right)^{\circ}=\left(162 \frac{1}{2}\right)^{\circ}$
$=162^{\circ}+\frac{1}{2}=162^{\circ} 30^{\circ} $
Angle between two consecutive marks
$=360^{\circ} / 12=30^{\circ}$
Angle traced by hour-hand in 35 minutes
$=\frac{7}{12}\left(30^{\circ}\right)=\left(\frac{35}{2}\right)^{\circ}=\left(17 \frac{1}{2}\right)^{\circ} \frac{1}{3}$
Angle between marks 1 and $7=6 \times 30^{\circ}=180^{\circ}$
Angle between two hands of the clock at thirty five
$ \text { past one }=180^{\circ}-\left(17 \frac{1}{2}\right)^{\circ}=\left(162 \frac{1}{2}\right)^{\circ}$
$=162^{\circ}+\frac{1}{2}=162^{\circ} 30^{\circ} $
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