oppositeshypotenuse

Opposite over hypotenuse, often called oppositeshypotenuse, is the ratio of the length of the side opposite a given angle to the length of the hypotenuse in a right triangle. In standard trigonometry, this ratio is defined as the sine of the angle: sin(θ) = opposite/hypotenuse. The term describes a fundamental relationship used to relate angles to side lengths.

To identify the opposite side and the hypotenuse, note that the hypotenuse is the side opposite the right angle. For a particular non-right angle θ in the triangle, the side opposite that angle is the side across from θ. If the opposite side has length a and the hypotenuse has length c, then sin(θ) = a/c. For example, if a = 3 and c = 5, sin(θ) = 3/5, so θ is approximately 36.87 degrees.

This ratio is central to solving problems in right triangles and is invariant under similarity (scaling) of the triangle. The opposite/hypotenuse ratio is one of the core definitions of the sine function, which can also be understood in broader contexts using the unit circle to extend to all angle measures. In addition to sine, other trigonometric ratios relate the opposite side to the hypotenuse through different definitions: cosine uses the adjacent side, and tangent uses the opposite and adjacent sides.