Question

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 metreswhen it has traced out 54o at the center, find the length of the rope.



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Answer 1

Step-by-step explanation:

ANSWER

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×

180

π

)=

5

2π

and S=88

∴θ=

radius

arc

⇒

5

2π

=

r

88

⇒r=

2π

88×5

=70

solution

Answer 2

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=54

0

and arc AB=88m

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

Now θ=54

=(54×

180

π

)=

5

2π

and S=88

∴θ=

radius

arc

⇒

5

2π

=

r

88

⇒r=

2π

88×5

=70