Trig Ratio Basics

Sine is the ratio of the length of the opposite side to the length of the hypotenuse. Formula: $$\text{sine} = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

Cosine is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: $$\text{cosine} = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .

Tangent is the ratio of the length of the opposite side to the length of the adjacent side. Formula: $$\text{tangent} = \frac{\text{opposite}}{\text{adjacent}}$$ .

The formula is: $$\text{hypotenuse} = \frac{\text{opposite}}{\text{sine}}$$ .

The formula is: $$\text{adjacent} = \text{hypotenuse} \times \text{cosine}$$ .

The formula is: $$\text{opposite} = \text{adjacent} \times \text{tangent}$$ .

Using sine: $$\text{opposite} = 50 \times \text{sine}(30°) = 25$$ .

Using cosine: $$\text{hypotenuse} = \frac{40}{\text{cosine}(60°)} = 80$$ .

Tangent can be expressed as: $$\text{tangent} = \frac{\text{sine}}{\text{cosine}}$$ .

The value is 1, since $$\text{tan}(45°) = \frac{\text{opposite}}{\text{adjacent}} = 1$$ .