Final answer:
To find the radian measure of the central angle given an arc length of 85 km and a radius of 35 km, the arc length is divided by the radius, resulting in a central angle measure of approximately 2.4286 radians.
Step-by-step explanation:
The question involves finding the radian measure of a central angle of a circle given the radius and the arc length intercepted by that angle. The formula used to find the radian measure (Δθ) is Δθ = arc length (αs) / radius (r). Since the arc length is given as 85 kilometers and the radius is given as 35 kilometers, we can directly substitute these values into the formula.
Δθ = s / r
Δθ = 85 km / 35 km
Δθ = 2.4286 radians
Therefore, the radian measure of the central angle is approximately 2.4286 radians.