Since the poles are 6 meters high and the clearance is 4 m, then the sag is 2 m.
We can use Newton's method to find the length.
The sag is given by
b is the distance from the origin to one of the poles. 5 m.
Try an initial guess for u. Then, once it converges, 'a' can be found by just subbing it into
The length can be found by plugging 'a' into the length formula:
We can derive the length by: