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Q. A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes $44\, metres$, when it has traced out $72^\circ$ at the centre, the length of the rope is

KCETKCET 2009Trigonometric Functions

Solution:

Length of arc $=2 \pi r \times \frac{\theta}{360^{\circ}}$
$\Rightarrow \,\,\,\,\,44=2 \times \frac{22}{7} \times r \times \frac{72}{360} $
$\Rightarrow \,\,\,\,\,r=\frac{44 \times 7 \times 5}{44}=35\, m$
which is the length of the rope.