Answer
Shadow angle of Fargo, North Dakota at 5:00 p.m.
= $69.8^{\circ}$
Work Step by Step
Formula given to calculate shadow angle $\theta$ is-
$\tan\theta$ = $\sin α . tan (h.15^{\circ})$
Given
Latitude of Fargo, North Dakota, α = $46.877^{\circ}$
Time = 5:00 p.m.
Therefore number of hours from noon, h = 5
Substituting these values in formula for shadow angle, $\theta$,
$\tan\theta$ = $\sin 46.877^{\circ} . tan (5\times15^{\circ})$
= $\sin 46.877^{\circ} . tan 75^{\circ}$
Using calculator-
$\tan\theta$ = $ (0.7298879341) \times (3.7320508076)$
= $2.7239788539$
Therefore-
$\theta$ = $\tan^{-1} (2.7239788539)$
=$ (69.841306693)^{\circ}$
Rounding to nearest tenth-
$\theta$ = $69.8^{\circ}$
