A hiker walks 11.54 m, E and 22.69 m, N. What is the direction of his resultant displacement?

To determine the direction of the hiker's resultant displacement, we need to find the angle θ of the displacement vector relative to the eastward direction. This angle can be calculated using trigonometry, specifically the tangent function, which relates the opposite and adjacent sides of a right triangle:

\[
\tan(\theta) = \frac{\text{opposite (north displacement)}}{\text{adjacent (east displacement)}} = \frac{22.69 \, \text{m}}{11.54 \, \text{m}}
\]

Let's calculate this angle.

\[
\theta = \tan^{-1}\left(\frac{22.69}{11.54}\right)
\]

Calculating this:

\[
\theta \approx \tan^{-1}(1.966) \approx 63.43^\circ
\]

Thus, the direction of the resultant displacement is approximately **63.43° north of east**.

Would you like further details or have any questions?

Here are some related questions:
1. How do we calculate the magnitude of the resultant displacement?
2. Why do we use the tangent function to calculate direction in this case?
3. How would the problem change if the hiker had walked west instead of east?
4. What trigonometric functions are used to solve right-angle triangle problems like this?
5. Can we use vector addition to find both magnitude and direction?

**Tip:** When working with directions in displacement problems, always keep track of the reference axis (like east or north).

Discover how to calculate the direction of a hiker's resultant displacement using trigonometry. In this problem, the hiker walks 11.54 m east and 22.69 m north. The angle of displacement is calculated using the tangent function and inverse tangent. This guide is suitable for students in Grades 9-11.

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