Trigonometric ratios depend on an angle, not on the size of a right triangle.
WHAT HAPPENS IF…Double the hypotenuse while holding the angle fixed. What changes?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideasinθ=hypopp,cosθ=hypadj,tanθ=adjopp
Right triangles with the same acute angle are similar. Corresponding side lengths scale by one common factor, which cancels in their ratios. The adjacent leg must be identified relative to the chosen angle.
A detail that matters
The hypotenuse is always opposite the right angle, not whichever side looks longest on a distorted drawing.