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There's something I'm having difficulty understanding in the triangulation method of finding distances. Just trying to understand the principle.

If two objects have the same apparent size and are placed at different distances, wouldn't our measurement of angles be the same for both?

E.g the sun and moon both have an approximately equal apparent size as viewed from Earth. But the sun is much farther away than the moon is. I can't visualize how, if measurements are made, different values of angles would be attained for the two cases i.e moon and sun.

I don't know why my intuition is compelling me to believe that if the apparent sizes of two objects are same, the angles will also be the same no matter how far apart the objects are...