The straight line 'tunnel' distance between the two cities is

${\displaystyle 2d=1.943713}$

${\displaystyle \sin \theta =\frac{d}{R}=0.97186}$

Hence

${\displaystyle \theta =1.33300\hspace{0.5em}\mathrm{radians}=76.{38}^o.}$

The angle between the radii to the 2 places is 2.666 radians so, taking the radius of the earth to be 6378 kilometres, the distance between London and Sydney is 17,000 kilometres to the accuracy of this calculation.

This distance is $R\Theta$ where $\Theta$ is the angle between the radii to the 2 places. At an altitude of 6 kilometres the distance is $(R+6)\Theta$ and the 'extra' distance is $6\Theta =16$ kilometres.