The height of the cable must be 76 meters.
Work Step by Step
As per the given statement , we have vertical height of the tower: $y=160$ and Diameter = 1280 meter. This implies that Radius: $2x=1280 \implies x=640$ Now, consider $x^2=4py$ This implies that $(640)^2=(4p)(160) \implies p=640$ As the cable 200 meters from a tower. This means that $x=640-200=440$ and $(440)^2=(4)(640)y \implies y=75.625 \approx 76$ Hence, the height of the cable must be 76 meters.