The tangent function is a mathematical function that relates the ratio of the length of the sides of a right triangle. Specifically, the tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In other words, if we have a right triangle with an angle θ, and the length of the adjacent side is a, and the length of the opposite side is b, then the tangent of θ is defined as b/a. The tangent function is commonly used in trigonometry and geometry to solve problems involving right triangles, as well as in calculus and other branches of mathematics.