Definition: SOH CAH TOA is a mnemonic for the three right-triangle ratios: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent.
What does each part mean?
- SOH: Sine = Opposite / Hypotenuse.
- CAH: Cosine = Adjacent / Hypotenuse.
- TOA: Tangent = Opposite / Adjacent.
How do you choose a ratio?
Mark the angle you are using. Label the three sides relative to it. Circle the two sides involved in the problem, one known and one unknown, and pick the ratio that contains exactly those two.
Example. In a right triangle, angle B = 38 degrees and the hypotenuse is 20. Find the side opposite B. The sides involved are opposite and hypotenuse, so use SOH: sin 38 degrees = x / 20, and x = 20(0.6157), about 12.3. For the adjacent side, use CAH: 20 · cos 38 degrees = 20(0.7880), about 15.8.
What mistakes occur?
Labeling opposite and adjacent from the wrong angle, and applying these ratios to triangles with no right angle. For those, use the law of sines or the law of cosines. Check that your answer is shorter than the hypotenuse.