What is the ratio for tangent?

The tangent ratio in trigonometry is a fundamental trigonometric ratio that compares the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle. It is defined as the ratio of the length of the opposite side to the length of the adjacent side:

tangent (θ) = opposite / adjacent

In the context of a right triangle, the tangent ratio can also be expressed as the ratio of the sine of an angle to the cosine of that angle:

tan(θ) = sin(θ) / cos(θ)

The tangent ratio is often abbreviated as "tan" and is commonly used in trigonometric functions and equations to solve for unknown sides or angles in right triangles. It is also used to calculate slope in mathematics and engineering applications.