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 88 metres when it traces 72° at the centre, find the length of the rope. ***************************

Answer 1

Angle in degree = 72o
Angle in radian = ​(π x 72)/180 = (π x 2)/5

θ = Length of arc/radius
2π/5 = 88 / r
r = (88 x 5 x 7) / (2 x 22) = 70 m Ans

Answer 2

The length of the rope is 70 meters.

Given:

Angle in degree $=72^{\circ}$

First, we will convert the angle given in degree into an angle in radian. This can be done by multiplying 72 by $\frac{180}{\pi}$.

Angle in radian $=\frac{(\pi \times 72)}{180}=\frac{\pi \times 2}{5}=\frac{2 \pi}{5}$

Now the formula for the calculation of angle, is:

$\theta=\frac{\text {Length of arc}}{\text {radius}}$

Substituting the values in this formula,  

${\frac{2 \pi}{5}=\frac{88}{r}} \\ \\ {r=\frac{88 \times 5 \times 7}{2 \times 22}=70 \mathrm{m}}\end{array}$

Therefore, the length of the rope is 70 meters.