Answer :
To determine the value of [tex]\(\tan 45^\circ\)[/tex], let's start by recalling the definition and properties of the tangent function.
The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For the specific case of [tex]\(\tan 45^\circ\)[/tex], we can use information from a 45-45-90 triangle. In this type of triangle, the lengths of the two legs are equal, and the hypotenuse is [tex]\(\sqrt{2}\)[/tex] times the length of either leg.
Thus, for a 45-45-90 triangle:
[tex]\[ \tan 45^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{1} = 1 \][/tex]
This agrees with our previously learned trigonometric values where [tex]\(\tan 45^\circ = 1\)[/tex].
Therefore, the correct answer to the question "What is [tex]\(\tan 45^\circ\)[/tex]?" is:
[tex]\[ \boxed{1} \][/tex]
The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For the specific case of [tex]\(\tan 45^\circ\)[/tex], we can use information from a 45-45-90 triangle. In this type of triangle, the lengths of the two legs are equal, and the hypotenuse is [tex]\(\sqrt{2}\)[/tex] times the length of either leg.
Thus, for a 45-45-90 triangle:
[tex]\[ \tan 45^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{1} = 1 \][/tex]
This agrees with our previously learned trigonometric values where [tex]\(\tan 45^\circ = 1\)[/tex].
Therefore, the correct answer to the question "What is [tex]\(\tan 45^\circ\)[/tex]?" is:
[tex]\[ \boxed{1} \][/tex]
