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=(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°.