Question

A ladder is leaning against the top of an 8.9 m wall. If the bottom of the ladder is 4.7 M from the bottom of the wall, then the angle between the ladder and the wall is

Answer 1

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

$\tan \theta=\frac{\text{opp}}{\text{adj}}$

From the triangle,

$\begin{gathered} \text{opp = 4.7} \\ \text{adj = 8.9} \end{gathered}$

Substituting these values, we have

$\begin{gathered} \tan \theta=\frac{4.7}{8.9} \\ \tan \theta=0.528 \end{gathered}$

We can then find the angle to be

$\begin{gathered} \theta=\tan ^{-1}(0.528) \\ \theta=27.8\degree \end{gathered}$

The angle between the ladder and the wall is 27.8°.