SOHCAHTOA
/ soh-kah-TOH-ah /
When you first meet sine, cosine, and tangent it is easy to forget which ratio uses which sides. SOHCAHTOA is a nonsense word built to fix that — a tidy mnemonic that packs all three definitions into eight letters you can chant.
Read it in three chunks: SOH means Sine = Opposite / Hypotenuse; CAH means Cosine = Adjacent / Hypotenuse; TOA means Tangent = Opposite / Adjacent. To use it, label the three sides of your right triangle relative to the angle you care about (the side facing the angle is opposite, the slanted longest side is the hypotenuse, the remaining leg is adjacent), decide which two sides your problem involves, and the mnemonic tells you which function links them. For example, if you know the opposite side and want the hypotenuse, the only chunk containing both is SOH, so sine is your tool.
It is a memory device, not a theorem, and it works only inside a right triangle — the labels opposite, adjacent, and hypotenuse have no meaning otherwise. For oblique (non-right) triangles you must switch to the law of sines or the law of cosines. Treat SOHCAHTOA as training wheels: useful at the start, but the unit-circle picture eventually replaces it.
A problem gives you the adjacent side (8) and the angle (30 degrees) and asks for the opposite side. The chunk with both 'opposite' and 'adjacent' is TOA, so tan 30 degrees = opposite / 8, giving opposite = 8 x tan 30 degrees ≈ 8 x 0.577 = 4.62.
Match the two sides in your problem to the one chunk that names both — that chunk's function is the one to use.
SOHCAHTOA never applies to the angle that equals 90 degrees, and it does not work in a triangle with no right angle at all — students often try it anyway and get nonsense.