Relations in right triangles

Pythagorean theorem

\[c^2 = a^2+ b^2\]

Trigonometric relations

Let $\theta$ be a general angle in a right triangle that is not right. Then

\[\cos(\theta)= \frac{\rm adjacent}{\rm hypothenuse} \qquad\qquad \sin(\theta)= \frac{\rm opposite }{\rm hypothenuse} \qquad\qquad \tan(\theta)= \frac{\rm opposite }{\rm adjacent}\]

Such that, in our example:

\[\cos(\alpha)=\frac{a}{c} \qquad\qquad \sin(\alpha)=\frac{b}{c} \qquad\qquad \tan(\alpha)=\frac{b}{a}\]

and

\[\cos(\beta)=\frac{b}{c}\qquad\qquad \sin(\beta)=\frac{a}{c} \qquad\qquad \tan(\beta)=\frac{a}{b}\]