Final answer:
To find the length of the arc for a 119 mile radius circle with an angle of 2.6 radians, apply the formula s = rθ, which gives an arc length of 309.4 miles.
Step-by-step explanation:
To determine the length of an arc in a circle given the radius and central angle in radians, we can use the formula for the arc length, s, which is the product of the radius, r, and the angle in radians, θ. In this case, the radius of the circle is 119 miles and the central angle is 2.6 radians. The formula for the arc length is given by s = rθ.
The calculation proceeds as follows:
- s = rθ = 119 mi * 2.6 radians
- s = 309.4 miles (since the unit of radians is dimensionless, the arc length will be in miles)
This calculation gives us the arc length associated with an angle of 2.6 radians in a circle with a radius of 119 miles.