Question

A horse is tied to a pole by a rope. How long must the rope be so that the horse
can move through 108 meters tracing an angle 75 degree on a circular path?

Answer 1

Answer: 70

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 ∠APB=72  

and arc AB=88m

Let r be the length of the slope i.e PA=rmeters

Now θ=72=(72× π/ 180  )=  2π/5  

​ and S=88

∴θ=arc/ radius   ⇒   2π/5  = 88/ r  

⇒r=  88×5 /  2π  

​  =70

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