Basic Trig Ratios

The hypotenuse is the longest side of a right triangle, opposite the right angle.

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse: $$\frac{opposite}{hypotenuse}$$ .

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: $$\frac{adjacent}{hypotenuse}$$ .

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side: $$\frac{opposite}{adjacent}$$ .

SOH CAH TOA helps remember: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

The sine of 30 degrees is $$\frac{1}{2}$$ .

The cosine of 60 degrees is $$\frac{1}{2}$$ .

The tangent of 45 degrees is 1, since $$\frac{opposite}{adjacent} = 1$$ .

In a 30-60-90 triangle, the sides are in the ratio 1 : $$\frac{\text{√3}}{2}$$ : 2.

In a 45-45-90 triangle, the sides are in the ratio 1 : 1 : $$\text{√2}$$ .