SOLUTION
Let us make a diagram to interpret the question, we have
From the diagram above, we can see that a right-angle triangle is formed between the light beam and the road.
The opposite side of the angle theta given is 5 inches and the adjacent side is 28 feet. So we have to convert the 28 feet to inches before solving we have
[tex]\begin{gathered} 1\text{ feet = 12 inches, so } \\ 28\text{ feet = 28}\times12=336\text{ inches} \end{gathered}[/tex]Using trigonometry SOHCAHTOA to find the angle theta, we have
[tex]\begin{gathered} TOA\text{ tan}\theta=\frac{opposite}{adjacent} \\ \text{tan}\theta=\frac{5\text{ inches }}{28\text{ feet}}=\frac{5\text{ inches}}{336\text{ inches }} \\ tan\theta=\frac{5}{336} \\ \theta=tan^{-1}\frac{5}{336} \\ \theta=0.85255 \end{gathered}[/tex]Hence the angle is 0.85 degrees to the nearest hundredth
