Let's begin by redrawing the diagram showing the angle of depression using the theory of corresponding angles:
Using trigonometric ratios, we have:
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\frac{opposite}{hypothenuse} \\ \cos \text{ }\theta\text{ = }\frac{adjacent}{hypothenuse} \\ \tan \text{ }\theta\text{ = }\frac{opposite}{adjacent} \end{gathered}[/tex]
We have the sides:
opposite side = 27
adjacent side = 19
Since we have opposite and adjacent sides we would use the tangent ratio.
Substituting we have:
[tex]\begin{gathered} \tan \text{ x = }\frac{27}{19} \\ x\text{ = }\tan ^{-1}(\frac{27}{19}) \\ x\text{ = }54.8658 \\ \approx54.87^0\text{ (nearest hundredth)} \end{gathered}[/tex]
Answer: 54.87 degrees
