Question

How do we know how far the sun and other planets are from the Earth?

Answer 1

We can approximate average distances of other planets from the Earth from the difference of average distances from the Sun.

Explanation:

The average distance of planets from the Sun in millions of km:
Mercury - 57.9, Venus - 108.2, Earth - 149.6, Mars - 227.9, Jupiter - 778.6, Saturn - 1433.5, Uranus - 2872.5 and Neptune - 4495.1.
Despite that there are mini/max variations, the average distances of the Earth from other planets are same as the differences of average distances from the Sun, as given below.
Earth - Mercury: 91.7, Earth - Venus: 41.4, Earth - Mars: 78.3, Earth - Jupiter: 629, Earth - Saturn{ 1283.9, Earth - Uranus: 2722.9 and Earth - Neptune: 4345.5.
Reference: Planetary Data, NASA.