Question

What is the approximate angular diameter of venus when it is a very slim crescent? (measure full diameter of the planet, not just the crescent)
a. 15â

b. 30â

c. 60â

d. 60â?

Answer 1

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