What is the correct ratio for tangent in relation to a right triangle?

In a right triangle, the tangent function is defined as the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle. This relationship can be visualized within the context of the triangle, where the "opposite" side is directly across from the angle of interest, while the "adjacent" side is next to that angle.

Understanding this ratio is critical in trigonometry, as it forms the basis for many calculations in physics and engineering, particularly in naval applications where understanding angles and forces is essential. The correct ratio, opposite/adjacent, allows one to determine the angle of inclination or various other properties of the triangle using trigonometric functions.

Consequently, the other ratios mentioned, including opposite/hypotenuse (which defines the sine function), adjacent/hypotenuse (which defines the cosine function), and hypotenuse/adjacent, do not accurately represent the tangent ratio in the context of a right triangle. Each of these ratios corresponds to different trigonometric functions but does not fulfill the definition of tangent specifically. Thus, recognizing that tangent equals opposite divided by adjacent is fundamental in solving many problems involving right triangles.