Third Side, Reply to Jen
posted by Count Iblis .
Hi Jen,
I've seen the drawing. My site is down at the moment.
Draw a line from Venus (either of the two positions) to the line EarthSun at right angles.
Let's call the distance Earth Venus d. Then you have a right angle triangle with a hypotenuse d, the line that intersects the line Sun Earth at right angles has a length of
d sin(30°)= d/2 and the distance from the Earth to the point where that line of length d/2 intersects the line Earth Sun (let's call it P) is
d cos(30°) =1/2 sqrt(3)d
The distance from the sun to P is then 1.5*10^8 km minus 1/2 sqrt(3)d
Now the line SunVenus is the hypotenuse of another right angled triangle with sides Sun to P and the line of length d/2 you've drawn.
This means that
(1.5*10^8 km  1/2 sqrt(3)d)^2 + (d/2)^2 = (distance from sun to venus) squared
You can then solve d from this quadratic equation.
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