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The system described in the question can be presented diagrammatically as shown below:
We can then bring out a diagram to solve as follows:
The angle θ is the required angle that we are to solve for.
We can use the Tangent Trigonometric Ratio to solve. The ratio is given to be
[tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]From the triangle,
[tex]\begin{gathered} \text{opp = 4.7} \\ \text{adj = 8.9} \end{gathered}[/tex]Substituting these values, we have
[tex]\begin{gathered} \tan \theta=\frac{4.7}{8.9} \\ \tan \theta=0.528 \end{gathered}[/tex]We can then find the angle to be
[tex]\begin{gathered} \theta=\tan ^{-1}(0.528) \\ \theta=27.8\degree \end{gathered}[/tex]The angle between the ladder and the wall is 27.8°.
