Finding vertical vs perpendicular distance for moments

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phospho
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Two-panel physics worked solution of a rod in equilibrium supported by strings at 30 and 60 degrees, with the centre of mass found from moments about a point where the string lines meet; the left panel shows x tan 30 and (4 - x) tan 60 as vertical distances, leading to x = 3 m.


The underlined red part: I don't particularly understand where they got this from?
The yellow highlight: Why are they finding the vertical distance, instead of the perpendicular distance?
 
The underlined red part follows from the definition of moment about a point. In the yellow part, what would the "perpendicular" distance be?