SOHCAHTOA: Your Triangle-Solving Toolkit

SOHCAHTOA breaks down into three essential ratios that connect angles to sides in right-angled triangles. Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent - these are the building blocks you'll use every time.

Before diving into calculations, you need to identify the three sides correctly. The hypotenuse is always the longest side (opposite the right angle), the opposite side sits across from your angle of interest, and the adjacent side sits next to your angle.

The five-step method makes solving triangles systematic and foolproof. Label your sides (OPP, ADJ, HYP), choose the right formula based on what you know and what you're finding, substitute your values, rearrange if needed, then calculate. Following this order prevents mistakes and builds your confidence.

Top Tip: When finding missing sides, multiply or divide to rearrange your equation. When the unknown is on top of the fraction, multiply both sides by the bottom number!

For missing angles, you'll use the inverse functions (sin⁻¹, cos⁻¹, tan⁻¹) on your calculator. If you know two sides, you can always find an angle - just choose the right ratio, substitute your values, then hit that inverse button to get your answer.