SOHCAHTOA: choosing the trig ratio
Name the three sides relative to the angle θ, then choose the ratio that connects the two sides you know or want: SOH for sine, CAH for cosine, and TOA for tangent.
A worked example
Always start from the angle θ. The hypotenuse is the longest side, directly across from the right angle; the opposite side is across from θ; and the adjacent side touches θ without being the hypotenuse. To find a missing side, suppose θ is 35° and the hypotenuse is 12 cm, and you want the opposite side. Opposite and hypotenuse appear together only in SOH, so sin 35° = x ÷ 12, which rearranges to x = 12 × sin 35° = 6.9 cm. To find a missing angle, suppose the opposite side is 5 m and the adjacent side is 8 m. That combination belongs to TOA, so tan θ = 5 ÷ 8 = 0.625, and the inverse function gives θ = tan⁻¹(0.625) = 32.0°. Recap: label the sides from θ, choose the ratio from the two sides involved, and then solve.
The mistake people actually make
Check that your calculator is in degree mode before you start, because in radian mode sin 35 returns −0.43 instead of 0.57. Use an inverse function such as tan⁻¹ only when the angle itself is the unknown.