Final answer:
The length of the arc intercepted by a central angle of π/3 radians in a circle with a radius of 15 m is approximately 15.7 m when rounded to the nearest tenth.
Step-by-step explanation:
The length s of an arc intercepted by a central angle can be found using the formula s = rθ, where r represents the radius of the circle and θ represents the angle in radians.
In this case, the radius r is given as 15 m and the angle θ is given as π/3 radians. Thus, we can calculate the arc length s as:
s = rθ = 15 m × (π/3) radians.
To find the numerical value of s, we use the approximate value of π, which is 3.14159.
s = 15 m × (3.14159/3)
s = 15 m × 1.0472
s ≈ 15.708 m
Therefore, rounding to the nearest tenth gives us s ≈ 15.7 m as the length of the arc.