Name the sides from the angle
The hypotenuse is opposite the right angle. For the chosen acute angle, the opposite leg faces it and the adjacent leg touches it. The hypotenuse is excluded from those two labels. Changing the acute reference angle swaps opposite and adjacent.
Use the ratio that contains the needed sides
For an acute angle θ in a right triangle, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent. Similarity explains why these ratios depend on the angle rather than the triangle’s size.
A mistake to avoid
These side-ratio definitions apply to a right triangle. Check that condition and the calculator’s angle unit before using a measured or calculated angle.
Worked example
Find an opposite side when sin θ = 0.6
If the hypotenuse is 10 cm, then opposite/10 = 0.6, so the opposite side is 6 cm. A similar triangle with a 20 cm hypotenuse would have a 12 cm opposite side, preserving the same ratio.