What is the value of tan 45?
Last Updated :
14 Mar, 2024
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.
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