You are on the Moon, observing Earth, at a distance of about 384,000 kilometers. Using the small-angle formula you conclude that the actual...

Denote the distance between the Moon and Earth as `D` and the diameter of Earth as `d.` We have an isosceles triangle with the legs of the length `D` and the base of the length `d.` Denote the angle between the legs as `alpha,` it is a small angle and we have to find it.

Then is is clear that  `tan(alpha/2)=(d/2)/D=d/(2D).`

It is true that for small angles `alpha`  `tan(alpha) approx sin(alpha) approx alpha.` Therefore `tan(alpha/2)=d/(2D)` implies `alpha/2 approx d/(2D),` or `alpha approx d/D.` In numbers it is equal to `(12,756)/(384,000) approx 0.033` radians. In degrees it is about `1.9.`