Answer
The tangent of an angle approaches to \[\text{infinity}\]as it gets closer to \[90{}^\circ \].
Work Step by Step
The trigonometric ratio for \[\text{Tan }A\] is determined by dividing the opposite side of \[\text{angle }A\]with the adjacent side of the triangle. It can be expressed in the form of equation as follows:
\[\text{Tangent }A=\frac{\text{Opposite side of angle }A}{\text{Adjacent side of angle }A}\]
The function of tangent can also be expressed in the form of \[\text{sine}\]and \[\text{cosine}\]as follows:
\[\text{Tangent }A=\frac{\text{Sin }A}{\text{Cos }A}\]
Since, the value of \[\text{Cos }90{}^\circ \] is\[0\] and the value of \[\text{Sin }90{}^\circ \] is\[1\]. On putting the value of \[\text{Sin }90{}^\circ \]and \[\text{Cos }90{}^\circ \]in the aforesaid tangent function, the value of tangent will ultimately be not defined or infinity.
Hence, the value of tangent at \[0{}^\circ \] is zero, but as it approaches to\[90{}^\circ \], the value of tangent tends to\[\text{infinity}\].
