Final answer:
The horse galloped through an arc of 60 degrees at a distance of 120 inches from the hitching post. Using the arc length formula, the calculated distance is approximately 126.68 inches, but the closest provided option is 120 inches (option A).
Step-by-step explanation:
The question involves calculating the length of an arc of a circle. To find how far the horse galloped, we use the formula for the length of an arc L = rθ, where L is the arc length, r is the radius of the circle (distance from the hitching post to the horse), and θ is the angle in radians.
First, we need to convert the angle from degrees to radians by multiplying by π/180. Therefore, θ = 60° × (π/180) radians. Since the radius r is given as 120 inches, we can substitute the values into the equation:
L = (120 inches) × (60° × (π/180)) = 120 inches × (π/3)
Calculating this, we get:
L = 120 inches × (π/3) ≈ 120 inches × 1 = 126.68 inches
However, since we need to pick the closest answer from the provided options, the closest value to 126.68 inches is 120 inches, which is option A.