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 meters when it traces the angle of 72° at the center, then the length of the rope is
1) 70m
2) 55m
3) 40m
4) 35 m
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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
0
and arc AB=88m
Let r be the length of the slope i.e PA=rmeters
Now θ=72
0 =(72× 180π)= 5
2π and S=88
∴θ= radius arc ⇒ 5
2πr = 88 ⇒r= 2π
88×5 =70
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