Right-Triangle Ratio Simulator
The trigonometric ratios are defined by shape, not size. This simulator lets you resize a right triangle while keeping its angles fixed, showing that sine, cosine and tangent do not budge.
How to use this simulation
- Change the angle θ
- Scale the whole triangle up and down
- Display each side length and the resulting ratios
What to look for
- Scaling the triangle changes every side but leaves the ratios unchanged
- sinθ and cosθ never exceed 1, since the hypotenuse is always the longest side
- tanθ grows without limit as the angle approaches 90°
The physics behind it
In a right-angled triangle, sinθ is opposite over hypotenuse, cosθ adjacent over hypotenuse, and tanθ opposite over adjacent. Because all triangles with the same angles are similar, these ratios depend only on the angle. That independence from size is what makes trigonometry usable for measuring inaccessible distances.