Answer:
55.7° southeast.
Explanation:
We can represent the situation with the following diagram
So, the direction of the displacement needed for the hiker to return to his starting point is given by angle θ. This angle can be calculated using the trigonometric function tangent as follows
[tex]\begin{gathered} \tan\theta=\frac{\text{ Opposite side}}{\text{ Adjacent side}} \\ \\ \tan\theta=\frac{66}{45} \\ \\ \tan\theta=1.47 \\ \\ \theta=\tan^{-1}(1.47) \\ \theta=55.7° \end{gathered}[/tex]
Therefore, the direction is 55.7° southeast.
