What is the value of tan 45°?

The value of tan 45° is 1 because, in a right triangle, the tangent function is defined as the ratio of the lengths of the opposite side to the adjacent side. At a 45° angle, both sides are equal in length, which means the ratio of the opposite side to the adjacent side is 1:1. Therefore, the value of the tangent at 45° is 1. This property is consistent in trigonometry, where the tangent of 45° is always equal to 1 due to the nature of a 45-45-90 triangle, where both angles measure 45° and both legs are of the same length.