We would apply the formula for determining the length of an arc which is expressed as
length of arc = θ/360 x 2 x pi x radius
From the information given,
radius = 4000
length of arc = 8000
θ is in degrees
pi = 3.14
By substituting the values into the formula, we have
8000 = θ/360 x 2 x 3.14 x 4000
8000 = 69.78θ
θ = 8000/69.78
θ = 114.65 degrees
The next step is to convert from degrees to radians. Recall
pi x radian = 180 degrees
We would multiply the degrees by pi/180. We have
114.65 x 31.4/180 = 2
The angle in radians is 2 radians