This year Venus was slim crescent in March when the Earth-Venus was about [tex]L=42*10^6 km[/tex] (the minimum distance)
To find its angular diameter we apply the trigonometry
[tex]\tan \alpha = D/L[/tex]
where D=21000 km is the planet diameter and L is the distance to the planet. For small angles we consider
[tex]\tan \alpha \approx \alpha [/tex]
Thus the angular diameter of venus when it was slim crescent was
[tex]\alpha =D/L =21000/(42*10^6) =2.9*10^{-4} rad[/tex]
In degrees this is
[tex]\beta =\alpha*180/\pi = 0.0167 degree[/tex]
We know that 3600 seconds correspond to 1 degree. Therefore
[tex]1''=1/3600 =2.8*10^{-4} degree[/tex]
Hence
[tex]\beta = 0.0167/2.8*10^{-4} =60.12''
[/tex]
Therefore the angular diameter of Venus when it was slim crescent was 60''.
