What is the value of tan(45°)?

The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. For an angle of 45°, the two sides are equal, meaning the opposite and adjacent sides have the same length. Thus, the ratio of the lengths results in 1, which corresponds to tan(45°) = 1.

Alternatively, in terms of the unit circle, at 45° (or π/4 radians), the coordinates are (√2/2, √2/2). The tangent function, defined as y/x, yields (√2/2) / (√2/2), which again simplifies to 1. This gives clear geometric and analytical reasoning that supports the conclusion that the value of tan(45°) is indeed 1.