Answer
Shadow angle of San Luis Obispo at 2:00 p.m.
= $18.4^{\circ}$
Work Step by Step
Formula given to calculate shadow angle $\theta$ is-
$\tan\theta$ = $\sin α . tan (h.15^{\circ})$
Given
Latitude of San Luis Obispo, α = $35.282^{\circ}$
Time = 2:00 p.m.
Therefore number of hours from noon, h = 2
Substituting these values in formula for shadow angle, $\theta$,
$\tan\theta$ = $\sin 35.282^{\circ} . tan (2\times15^{\circ})$
= $\sin 35.282^{\circ} . tan 30^{\circ}$
Using calculator-
$\tan\theta$ = $ (0.5776011987) \times (0.5773502692)$
= $0.3334782076$
Therefore-
$\theta$ = $\tan^{-1} (0.3334782076)$
=$ (18.442419111)^{\circ}$
Rounding to nearest tenth-
$\theta$ = $18.4^{\circ}$
