What Is SOH CAH TOA?
SOH CAH TOA is a simple mnemonic device used to remember the three fundamental trigonometric functions used to solve right-angled triangles.
The Three Ratios Breakdown
SOH (Sine)
Formula
Sin(θ) = Opposite ÷ Hypotenuse
Use sine when you know or need to find the side opposite to the angle θ relative to the longest side (hypotenuse).
CAH (Cosine)
Formula
Cos(θ) = Adjacent ÷ Hypotenuse
Use cosine when working with the side adjacent (next to) the angle θ and the hypotenuse.
TOA (Tangent)
Formula
Tan(θ) = Opposite ÷ Adjacent
Use tangent when working directly with the two leg sides of the right triangle without needing the hypotenuse.
Step-by-Step Triangle Example
Consider a right triangle with an angle θ = 30° and a hypotenuse of 10 meters.
- Find Opposite Side: Sin(30°) = Opposite ÷ 10 → 0.5 = Opposite ÷ 10 → Opposite = 5m.
- Find Adjacent Side: Cos(30°) = Adjacent ÷ 10 → 0.866 = Adjacent ÷ 10 → Adjacent = 8.66m.