Answer
$78.7^\circ$
Work Step by Step
Given equation is-
$\tan\theta$ = $5$
The tangent function is one-to-one on the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$ , so there is only one solution of the equation with $\theta$ between $0^\circ$ and $180^\circ$. To find that taking $\tan^{-1}$ of each side-
$\theta$ = $\tan^{-1}5$
Using calculator in degree mode-
$\tan^{-1}$ → $5$ = 78.690067526
i.e. $\theta$ = $\tan^{-1}5 \approx 78.7^\circ$
(Rounded to one decimal place)
