Final answer:
To find the arc length, we use the formula (s = rθ) with the values given (radius = 14 meters, angle = 5π/6 radians), resulting in an arc length of approximately 36.63 meters.
Step-by-step explanation:
The length of an arc in a circle can be found using the formula:
Arc length (s) = radius (θ)
Given the radius (r) as 14 meters and the central angle (θ) as 5π/6 radians, we can calculate the arc length by substituting these values into the formula.
θ = (5π/6 radians) × (14 meters)
θ = (5π/6) × 14
θ = (5×14π)/6
θ = 70π/6
θ = (35π/3)
θ ≈ 36.63 meters (using π ≈ 3.14159)
The arc length is approximately 36.63 meters.