What is the value of tan 45?

The value of tan 45° is 1.

To find the value of tan45∘, we consider a right-angled triangle where one of the angles is 45°. In a 45-45-90 triangle, the two acute angles are equal, and the sides opposite these angles are also equal.

Let’s consider a triangle where the angle is 45°. If we denote the length of the side opposite the angle as a and the length of the adjacent side as b, in a 45-45-90 triangle, a = b.

The tangent of an angle (⁡tan) is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

tan 45° = opposite side/adjacent side = a/b = b/b = 1

Therefore, the value of tan45∘ is 1. This is a unique property of 45-45-90 triangles, where the ratio of the side opposite to the adjacent side is always 1.