A steel cable one square inch in cross section and a mile long weighs <19k lb on Earth, a bit less on Venus. Cheap mild steel has tensile strength 50k lb/in², and can be as much as 10x as strong. So, self-supporting steel 3 miles to 30 miles.
Getting 250 tons of high-strength steel cable (sheathed against corrosion) to Venus is left as an exercise for the reader. Likewise, a big enough balloon to hold that up. And a strong enough winch.
But in practice, you would make the cable of carbon extracted from atmospheric CO2, instead, and it could support itself all the way down to the surface, 50 mi below. You would need to protect the end against acid vapor corrosion at 470 C: another exercise for the reader.
Getting 250 tons of high-strength steel cable (sheathed against corrosion) to Venus is left as an exercise for the reader. Likewise, a big enough balloon to hold that up. And a strong enough winch.
But in practice, you would make the cable of carbon extracted from atmospheric CO2, instead, and it could support itself all the way down to the surface, 50 mi below. You would need to protect the end against acid vapor corrosion at 470 C: another exercise for the reader.