Lets see how to get the following result:

We've been given::

We start from the coloured rectangle triangle

Being a rectangle triangle, we apply trigonometric reasons to the angle
and we obtain .
Being a small value, we can take the approx:
So, from what we saw before, we can conclude that and as , then we have that .
We are seeking for the Moon's diameter (we've called it 'D' in the figure.
We already know that the diameter is two times the radius, so .
If we substitude:.
And when we find out D: .