Answer:
31 foot
Step-by-step explanation:
Radius of the circular path = 15 feet
Angle of horse travel on a circular path = [tex]\frac{2\pi }{3}[/tex] radians = Central Angle
Central angle = [tex]\frac{2\pi}{3} \times \frac{180}{\pi}[/tex] degrees = 120°
Distance travelled by the carousel horse on the circular path over an angle of [tex]\frac{2\pi}{3}[/tex] = Arc length
We can use the formula below to calculate arc length;
°[tex]\frac{Central Angle}{360} = \frac{Arc length}{2\pi r}[/tex]
[tex]\frac{120}{360} = \frac{Arc length}{2\pi\times 15}[/tex]
Arc length =[tex]10\pi[/tex]
Arc length = 31.4 foot
Arc length (rounded to the nearest foot) = 31 foot
