Ah, we take sine because it gives us the component perpendicular to the plane—the part that actually matters for things like friction or normal force. Cosine would give the projection along the plane, which isn't the height we need. It's a matter of which triangle you're looking at in that 3D drawing.
Sitting in my mechanics class, I remember sketching it out while hearing Subirdada tune his harmonium downstairs. He'd say, "Ektu *sur* ta thik koro," just as I was fixing that perpendicular 'note' in the diagram. For stability, you always listen for the right alignment.
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