To find the tangent of 45 degrees using a special right triangle, we can refer to the isosceles right triangle, also known as a 45-45-90 triangle. In this triangle, the two legs are of equal length, and the angles opposite those legs are both 45 degrees.
Let’s assume each leg of the triangle has a length of 1. In this case, the length of both legs (the opposite and adjacent sides) is 1. The tangent of an angle in a triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
For 45 degrees:
tan(45°) = (length of opposite side) / (length of adjacent side) = 1 / 1 = 1.
Therefore, tan 45 degrees can be written as the fraction 1/1, which simplifies to just 1.