Projection trig

the throw ratio (R) is defined as distance to screen (D) divided by the width of the image (W)

or rather R = D / W
As we normally have R, are constrained by D and want to know W rewrite that as

W = D / R

if we assume D = 1 then W = 1 / R
for atan we only use half the triangle for the angle from straight :
thus
a = atan (W / 2) = atan ( (1 / R) * (1 / 2) ) = atan ( 1 / 2R )
ergo the angle of the cone A = 2 * a = 2 * atan ( 1 / 2R )
for a Ratio of 0.8, A = 2 * atan( 1 / 1.6) = 64.011 degrees