Which ratio defines tangent (tan) in a right triangle?

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. This relationship can be expressed mathematically as:

[

\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}

]

This definition is central to trigonometry and helps in solving various problems involving right triangles. The opposite side is the side that is directly across from the angle of interest, while the adjacent side is the side that forms the angle with the hypotenuse.

Understanding this ratio is essential for applying tangent in practical scenarios, such as calculating heights and distances in real-life applications. It allows you to find the tangent of an angle knowing the lengths of the sides of the triangle, which is particularly useful in contexts like surveying and physics.