What is the definition of the tangent function in relation to a right triangle?

The tangent function 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 you take an angle \( \theta \) in a right triangle, then the tangent of \( \theta \) is expressed as \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \). It’s a handy way to relate the angles of the triangle to the lengths of its sides! Understanding the tangent function doesn’t just stop at geometry classes; it's super useful in fields like architecture and engineering! When designing structures or analyzing slopes, the tangent helps in determining angles and ensuring stability. Using the ratio of heights to base lengths keeps everything balanced and sturdy – no wobbly buildings, please!