Mobile GSM phones are well capable of talking to towers on the ground at 35k feet. That's only about 10 kilometres. There will likely also be several towers within roughly equal distance with good line of sight. Indeed, one part of the reason mobile phones have been banned in aircraft for so long is because they would interfere with the *ground*. The fear being that having thousands of stations moving fast overhead, in range of potentially dozens of towers at the same time and roaming across them, would be too taxing for GSM to handle, causing service issues.
I've had phone conversations with people in aircraft, at altitudes of around 20k to 25k feet (6.1 to 7.6 kilometres), with them ringing on their GSM phones and it worked fine.