The maximum length of the corresponding arc can be found to be 15.630 miles.
How to find the length of the arc ?
To find the maximum length of the corresponding arc, you can use the formula for the length of a circular arc:
Arc Length (S) = (θ/360) * 2πr
θ is the angle in degrees (128° in this case)
r is the radius of the circle (maximum range of the lighthouse, which is 7 miles in this case)
S = (128/360) * 2 * 3.14 * 7
S = (128/360) * 43.96
S = 0.35556 * 43.96
S = 15.630 miles
In conclusion, the maximum length of the corresponding arc is approximately 15.78 miles when rounded to the nearest hundredth.