SOHCAHTOA

SOHCAHTOA is the standard memory device for the right-triangle definitions of sine, cosine, and tangent. Break it into three chunks: SOH — sin θ = opposite / hypotenuse; CAH — cos θ = adjacent / hypotenuse; TOA — tan θ = opposite / adjacent.

The labels are always relative to the angle you're working with. The hypotenuse is the longest side, opposite the right angle, and never changes. The opposite side is the one across from your angle, and the adjacent side is the leg next to it. In a 3-4-5 right triangle, for the angle across from the side of length 3: sin θ = 3/5, cos θ = 4/5, and tan θ = 3/4. Switch to the other acute angle and opposite and adjacent trade places.

These three ratios let you solve right triangles: given one acute angle and any side, you can find the remaining sides, and given two sides, an inverse trig function recovers the angle. SOHCAHTOA also anchors useful identities — tan θ = sin θ / cos θ follows directly from the definitions — and it is the bridge to the unit circle, where sine and cosine become coordinates.

Right-triangle trigonometry is a reliable scoring area on college admissions tests. The ACT, SAT, and CLT all ask questions that reduce to picking the correct SOHCAHTOA ratio — identifying which side is opposite versus adjacent, setting up the ratio, and solving. Practicing until the setup is automatic turns these into some of the fastest points on the test.