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 describes 88 metres when it traces ${72}^{\circ }$ at the centre, find the length of the rope.

Answer 1

Let us denote the post by P and let PA be the length of the rope in the tightest position. Suppose that the horse moves along the arc AB so that $\angle APB={72}^{\circ }$ and arc AB = 88 m.

Let the length of the rope P A be r metres.

Then, $\theta ={72}^{\circ }={(72\times \frac{\pi }{180})}^c={\left(\frac{2\pi }{5}\right)}^c\text{and}l=88m$

$\therefore r=\frac{1}{\theta }=\frac{88}{\left(\frac{2\pi }{5}\right)}m=(88\times \frac{5}{2}\times \frac{7}{22})m=70m$