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Imagine building a 30∘30^\circ skateboard ramp that is 10 feet long, and an architect building a massive 30∘30^\circ bridge ramp that is 1,000 feet long.
Even though one ramp is 100 times larger, the ratio of their heights to their ramp lengths is completely identical.
How can two completely different sized triangles share the exact same proportion?

Naming the Sides

In any right-angled triangle, every side has a name based on its position relative to a reference angle, which we often label with the Greek letter theta (ΞΈ\theta).
The hypotenuse is always the longest side across from the 90∘90^\circ square corner, the opposite side sits directly across from angle θ\theta, and the adjacent side is next to θ\theta.
Now that we know the names of the sides, how do we compare the opposite height to the hypotenuse length?

The Sine Ratio

The sine of an angle (abbreviated as sin⁑\sin) is simply a fraction comparing the length of the opposite side to the length of the hypotenuse.
sin⁑(θ)=OppositeHypotenuse\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}
Around 500 CE, Indian mathematician Aryabhata studied lengths of half-chords in circles called jya-ardha, which later evolved through Arabic and Latin translations into our modern word sine.
Why doesn't this fraction change when a triangle gets bigger or smaller?