Answer
The angle of elevation of the sun in the sky over New Orleans is $32.4^{\circ}$
Work Step by Step
Using the information from example 5:
$D = -0.1425$
$\omega = 0.7854$
We can convert $30^{\circ}$ to units of radians:
$L = (30^{\circ})(\frac{\pi~rad}{180^{\circ}}) = \frac{\pi}{6}~rad$
We can find $\theta$, the angle of elevation of the sun in the sky:
$sin~\theta = cos~D~cos~L~cos~\omega+sin~D~sin~L$
$sin~\theta = cos~(-0.1425)~cos (\frac{\pi}{6})~cos~(0.7854)+sin~(-0.1425)~sin~(\frac{\pi}{6})$
$sin~\theta = 0.535155$
$\theta = sin^{-1}(0.535155)$
$\theta = 32.4^{\circ}$
The angle of elevation of the sun in the sky over New Orleans is $32.4^{\circ}$
