TL;DR: Because light doesn't travel at an infinite speed.
Light travels at exactly 299,792,458 meters per second, and one AU is equal to 149,597,870,700 meters. Therefore, it takes about 500 seconds, or 8 minutes and 20 seconds, for light to travel from the Sun to Earth.
We know, precisely, the ratio between the Earth-Venus and Venus-Sun distances. Kepler's laws give us this.
We know, in terms of apparent size in the sky, the precise size of the Sun in degrees - just by looking at it.
Placing Venus between the Sun and the Earth, we can look at it from one point in the Earth (call it $N$) and see Venus against the Sun at a ...