Question

# A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describe $88metres$ when it traces $72°$ at the centre, find the length of the rope.

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Solution

## $\theta =72×\frac{\mathrm{\pi }}{180}=\frac{2\mathrm{\pi }}{5}$If $r$ be the radius of the circle,Then, $⇒\theta =\frac{l}{r}\phantom{\rule{0ex}{0ex}}⇒\frac{2\mathrm{\pi }}{5}=\frac{88}{r}\phantom{\rule{0ex}{0ex}}⇒r=\frac{88×5}{2\mathrm{\pi }}\phantom{\rule{0ex}{0ex}}⇒r=\frac{88×5}{2}×\frac{7}{22}\phantom{\rule{0ex}{0ex}}⇒r=70m$Hence, the length of the rope is $70m$.

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