Final answer:
The tangent function for a right triangle is given by the equation tan(theta) = y/x, where y is the length of the opposite side and x is the length of the adjacent side of the right triangle.
Step-by-step explanation:
The Tangent Function in Right Triangles
The equation that describes the tangent function for a right triangle is d. Tan theta equals opposite divided by adjacent. In the context of a right triangle with sides labeled x as the adjacent side, y as the opposite side, and h as the hypotenuse, the definition of the tangent of an angle (theta) is the ratio of the length of the opposite side to the length of the adjacent side. To put it into an equation, this is tan(theta) = y/x. The tangent function is one of the three primary trigonometric functions, the other two being sine and cosine, which are based on other ratios in a right triangle.
Understanding the roles of these functions is important not only in trigonometry but also in various applications like physics, where they are used to resolve vectors into scalar components or to predict results consistently across different principles.
The Pythagorean theorem, which states that a² + b² = c², can also be related to trigonometric functions as it represents the relationship between the lengths of the sides of a right triangle. However, this theorem is not used to define the trigonometric functions directly but rather connects the sides of the triangle under the rule of right-angled triangles.