Answer:
The horse travels 31 feet over an angle of radians
Step-by-step explanation:
- The formula of the length of an arc is L =
× 2πr, where x is the central angle subtended by this arc and r is the radius of the circle
- To change the angle from radian measure to degree measure multiply it by
∵ A carousel horse travels on a circular path
- That means the distance that the horse travels is the length
of an arc of the circular path
∵ The radius of the circular path is 15 feet
∴ r = 15 ft
∵ The horse travel over an angle of radians
- Let us change it to degree by multiply it by
∵ ×
=
= 120°
- use the formula above to find the distance
∵ d = × 2πr
∵ x = 120°
∴ d = × 2π × 15
∴ d = 10π
∴ d = 31.41592654 feet
- Round it to the nearest foot
∴ d = 31 feet
The horse travels 31 feet over an angle of radians