In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
For a 45-degree angle in a right triangle, in which the other acute angle is also 45 degrees (because the sum of the angles in a triangle is 180 degrees), the opposite side and the adjacent side are equal in length.
Therefore, the tangent of 45 degrees in this triangle is:
tan
(
4
5
∘
)
=
length of opposite side
length of adjacent side
=
1
1
=
1
tan(45
∘
)=
length of adjacent side
length of opposite side
=
1
1
=1
So, the correct answer is A. 1.
