Oppositehypotenuse

Oppositehypotenuse is a nonstandard term sometimes used informally in geometry to describe the ratio of the length of the side opposite a given acute angle to the length of the triangle’s hypotenuse in a right triangle. In many teaching contexts the phrase is used as a mnemonic for sine: opposite over hypotenuse.

In a right triangle with an acute angle A, let a be the side opposite A, b the side adjacent to A, and c the hypotenuse (the side opposite the right angle). The Pythagorean theorem states a^2 + b^2 = c^2. The value described by oppositehypotenuse corresponds to the sine of angle A, defined as sin(A) = a/c.

The oppositehypotenuse ratio ranges from 0 to 1 as angle A varies from 0° to 90°. It is a fundamental component of the primary trigonometric functions, connecting angle measures to side lengths. In the unit circle, sine values also describe the y-coordinate of points on the circle, illustrating the geometric meaning of the opposite-to-hypotenuse relationship.

Because "oppositehypotenuse" is not standard terminology, it can cause confusion with the distinct concepts of opposite side and hypotenuse. In formal contexts, it is clearer to refer separately to the opposite side, the hypotenuse, and to define sine as the ratio of opposite to hypotenuse. See also sine, cosine, tangent, and the Pythagorean theorem.