Question

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↗Question from class 11 maths ➡TRIGONOMETRY ⬅

Q.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 88m when it has traced out 72 degrees at the centre , find the length of the rope ...

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Answer 1

let the post be at point P and let PA be the length of rope in tight position . Suppose the horse moves along the arc AB such that angle
APB=72° and arcAB=88m let r be the length of rope I.e PA=r
then
angle APB=72°
=
${(72 \times \frac{\pi}{180} )}^{c} = { (\frac{2\pi}{5}) }^{c } \\ angle = \frac{ arc}{radius} \\ \frac{2\pi}{5} = \frac{88}{r} (radius = length) \\ r = \frac{88 \times 5}{2\pi} \\ r = 70m \\ hence \: length \: of \: the \: rope \\ is \: 70m$