A horse is tied to a pole with the help of a rope measuring 22 m. The horse moves in a circular path keeping the rope tight and covers a distance of 66 m. Find the angle (in degrees) traced out by the horse at the pole while moving.

let r be the radius of the circular path. AB be the length of the rope. AB = 22 m
distance covered = 66 m
therefore $2\pi r=66$
$$\begin{gathered} 2*\frac{22}{7}*r=66 \\ r=\frac{21}{2}=10.5 m \end{gathered}$$
OB = r =10.5
let the angle traced out by the horse be $\theta$ i.e. ABO
​let OA be the pole which is vertically standing on the horizontal circular plane.
OB is horizontal line.
angle AOB is 90 deg
$$\begin{gathered} \cos \theta =\frac{OB}{AB} \\ \cos \theta =\frac{10.5}{22}=\frac{21}{44} \\ \theta ={\cos }^{-1}\frac{21}{44} \end{gathered}$$

hope this helps you