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Q.
The large hand of a clock is $42 \,cm$ long. How much distance does its extremity move in $20$ minutes?
Trigonometric Functions
Solution:
The large hand of the clock makes a complete revolution in $60$ minutes.
$\therefore $ Angle traced out by the large hand in $20$ minutes (of time)
$=\frac{360^{\circ} \times 20}{60}=120^{\circ}=\frac{120\,\pi}{180}$ radian
$=\frac{2\pi}{3}$ radian
Hence, the distance moved by the extremity of the large hand $=\left(42\right)\times\frac{2\pi}{3}=88\,cm$. $\quad\left(\because l=r\theta\right)$