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 $88metres$ when it has traced out ${72}^o$ at the center, find the length of the rope.

Answer 1

Let the post be at point $P$ and let $PA$ be the length of the rope in tight position. Suppose the horse moves along the arc $AB$ so that $\angle APB={72}^0$ and arc $AB=88m$
Let $r$ be the length of the slope i.e $PA=rmeters$

Now $\theta ={72}^0=(72\times \frac{\pi }{180})=\frac{2\pi }{5}$
and $S=88$

$\therefore \theta =\frac{arc}{radius}\Rightarrow \frac{2\pi }{5}=\frac{88}{r}$

$\Rightarrow r=\frac{88\times 5}{2\pi }=70$