oppositeadjacent

Oppositeadjacent is a nonstandard term sometimes used to describe the relationship between the opposite and adjacent sides of a right triangle with respect to a given acute angle. It is not a formal name in most mathematical texts, where standard language refers to the “opposite side,” the “adjacent side,” and the “hypotenuse.” The term may be encountered in informal discussions, classroom notes, or problem statements as a shorthand for either the pair of sides or the ratio between them.

In a right triangle, let theta be an acute angle, o the length of the side opposite theta, and a the length of the side adjacent to theta (the leg that forms theta with the hypotenuse). The key trigonometric relationships are:

- tan(theta) = opposite/adjacent = o/a

- sin(theta) = opposite/hypotenuse = o/h

- cos(theta) = adjacent/hypotenuse = a/h

If used to denote a ratio, oppositeadjacent can be read as the o:a ratio, which corresponds to tan(theta). If used to denote the side pair, it refers to the two legs that are opposite and adjacent to theta, respectively.

Examples illustrate its use: in a right triangle with theta = 30 degrees, if o = 1 and a = sqrt(3), then tan(theta) = 1/√3, and the oppositeadjacent ratio is 1:√3. Practically, most mathematical writing would replace oppositeadjacent with “the ratio opposite to adjacent” or simply refer to the tangent function.

See also: opposite side, adjacent side, tangent, sine, cosine, trigonometric ratios.