SOH CAH TOA, finally explained

Published October 2026.

SOH CAH TOA is three sentences pretending to be one word. Unpacked: Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent.

Label from the angle

Pick your angle first, “opposite” and “adjacent” change depending on which angle you chose. The hypotenuse is always across from the right angle. Students who label before choosing an angle mix up opposite and adjacent; choose the angle, then label.

Worked example

A 5 m ladder leans against a wall at 70° to the ground. Height reached = 5 × sin 70° ≈ 5 × 0.940 = 4.70 m. Sine, because height is opposite the 70° angle and the ladder is the hypotenuse.

The one check that catches errors

For acute angles, sine and cosine are always between 0 and 1. If your calculator shows sin 30° = −0.99, you are in radian mode, switch to degrees. Try it live in our sin cos tan calculator.