How Does Calculating angular size without trigonometry Work?

You can figure out how big something looks in the sky by using simple ratios and a little imagination, just like comparing two pieces of candy.

Imagine you have a popsicle stick that’s 10 inches long, and you hold it up to your eye so it lines up with something far away, like a tree. If the tree looks exactly as big as the popsicle stick from where you’re standing, then you can say they're similar in size, one is just closer!

Now imagine that popsicle stick is like a ruler for the sky. If you know how far away the tree is (say, 10 feet), and it looks the same as your popsicle stick from that distance, then you can guess how big the tree really is.

This idea works with things in the sky too! Instead of a tree, imagine a moon or a plane. If you know how far away something is (like 200 miles), and you have a stick or your hand that you use to compare its size, just like comparing two pieces of candy, then you can figure out how big it looks in the sky without needing any tricky math.

So, even though there’s no magic, just clever comparisons using things you know, like sticks and candy, you can work out how something appears in the sky!