SOH-CAH-TOA

Property To remember the three main trigonometric ratios, use the mnemonic SOH CAH TOA. $$ \operatorname{sin} \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \quad (SOH) \\ \operatorname{cos} \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \quad (CAH) \\ \operatorname{tan} \theta = \frac{\text{Opposite}}{\text{Adjacent}} \quad (TOA) $$.

Explanation This is a super helpful memory trick! SOH CAH TOA stands for Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent. It's the key to matching the right trig ratio with the correct sides of a right triangle, making homework feel like less of a puzzle and more of a win.

Examples In a right triangle with angle B, opposite leg = 5, adjacent leg = 12, and hypotenuse = 13: $$ \operatorname{sin} B = \frac{5}{13} \text{ and } \operatorname{cos} B = \frac{12}{13} $$. For angle A in a right triangle with opposite leg = 20 and adjacent leg = 21, the tangent is: $$ \operatorname{tan} A = \frac{20}{21} $$. Given a right triangle with angle A, opposite leg = 8, and hypotenuse = 17, the sine is: $$ \operatorname{sin} A = \frac{8}{17} $$.