SOHCAHTOA and Finding Angles

SOHCAHTOA breaks down the three main trigonometric ratios you'll use constantly. Sine equals opposite over hypotenuse, Cosine equals adjacent over hypotenuse, and Tangent equals opposite over adjacent.

Remember, you can only use these ratios on right-angled triangles. The hypotenuse is always the longest side (opposite the right angle). The adjacent side sits next to your angle of interest, whilst the opposite side sits across from it.

When you're finding an unknown angle, you'll use the inverse functions: sin⁻¹, cos⁻¹, or tan⁻¹. For example, if cos x = 3/8, then x = cos⁻¹(3/8) = 67.98°.

The worked examples show this perfectly - whether you're using cosine $adjacent/hypotenuse$, tangent $opposite/adjacent$, or sine $opposite/hypotenuse$, the process stays the same. Identify your sides, pick the right ratio, then use the inverse function to find your angle.

Top Tip: Always double-check which side is which before choosing your trigonometric ratio - getting the adjacent and opposite mixed up is the most common mistake!