Parallax in cosmology a2 edexcel

How can I calculate the distance of the star and the sun using the diagram? I am confused because there are two angles of different degress and I dont know how yo apply the trigo to soove this @@

and How can I variable star, e.g, Cepheid that has a luminosity that varies with time, acts as a standard candle for us to calculate the distance of a star to earth? I know Cepheid has a periodic luminosity but what information can i get? Does it mean that I can deduce the distance of Cepheid to earth just from the luminosity??

Thank you!
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here's a better diagram imo.



obv you have to do some squashing to fit 3d space onto a 2d diagram so nothing's perfect.

what it's showing...

first of all you take a load of photographs over several years and notice nearby star has an apparent regular motion (period = 1 year) against the background of distant galaxies - that;s represented by the ellipse on the RHS of the diagram.

twice a year nearby star is going to be at 90 degrees to the line connecting earth and sun - there's a plane passing through the sun at 90 degrees to the earth and the plane is rotating with a period of one year - this plane sweeps everything in the sky in 6 months. You take a photo (A) of nearby star on one of these occasions.

three months later and the earth is where that plane was crossing the path of earth's orbit at the time you took your photo A - you take another photo (B) at this time.

you can measure the angular distance π nearby star has apparently moved by comparing the photos A&B and because one of the angles is a right angle you can apply simple trig to get a distance to nearby star in AU (AU = earth's orbital radius)

π is angular distance here - which is not the constant π 3.141... just call the angle theta in your diagram.