Hypotenuse, opposite and adjacent

Consider a right-angled triangle, and denote the interior angles different from $90^\circ$ by $\alpha$ and $\beta$ . We now introduce a naming convention for the sides of the triangle.

The longest side $c$ is, as already defined in the last section, the hypotenuse. The two smaller sides also have names, but these names are relative to the angle $\alpha$ or $\beta$ .

Definition 1

The side $a$ is called the adjacent side of $\alpha$ , and the opposite side to $\beta$ . Similarly, the side $b$ is called the adjacent side of $\beta$ and the opposite side to $\alpha$ .

This is shown in the figure below.

The opposite side is often denoted by $O$ , the adjacent side by $A$ , and the hypotenuse by $H$ .

Exercise 1

Indicate the reference angle with $\alpha$ , and complete labelling the sides with $A, O$ or $H$ .

Solution