Measuring Maximum Angle between Venus and Sun . . . . tov

As the earth and Venus go around the sun, the relative position of Venus with respect to the sun changes. At certain times of the year, Venus is a morning star, being visible before the sun rises. In other months it is an evening star. From September 18th 2003 Venus appears as an evening star.

We measure the angle which Venus makes with the horizon at the moment when the Sun sets. This angle increased from September to the end of March. Venus reached maximum height towards the end of March 2004.
We can measure the angle directly with our angle-dangle meter. It turns out to be approximately 45 degrees , towards the end of March 2004. (See B.5)
Another way to measure the angle is to measure the time between the setting of the sun and the setting of Venus. The maximum time turns out to be approximately three hours.
Since the earth rotates once in 24 hours, the stars and the sun appear to move through an angle of 360 degrees in 24 hours. They appear to move through 15 degrees (360 degrees divided by 24 hours) in one hour. The maximum three hours time difference between the two setting times means that the maximum angle between the Sun and Venus is approximately 45 degrees
From these measurements, and a few plausible assumptions, (like the assumption that the earth and Venus go around the sun in circles with the sun at the center), we can calculate that the sun - Venus and the sun - earth distance are approximately in the ratio 1 : 1.414. (See B.5)
What this means is that at the time of transit the Earth-Venus distance and the sun earth distance are in the ratio 0.414 : 1.414. From the properties of similar triangles we calculate that Venus appears to be magnified by a factor of 1.414/0.414, which is approximately 3.4.