Similar triangles and ratio basis
In a right triangle, the ratio between any two sides depends only on the triangle's angles, not its size: two right triangles that share an acute angle are similar, so their corresponding side ratios must be equal, which is exactly why a ratio like "opposite over hypotenuse" can be defined for an angle alone, without reference to any specific triangle, like a 30-60-90 triangle, whose opposite-over-hypotenuse ratio for its 30-degree angle is always 0.5, no matter how big the triangle is.
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