Final answer:
The question is about calculating a hiker's total displacement and direction after walking two segments with specific directions and distances, using vector addition and trigonometry.
Step-by-step explanation:
The question asks about determining a hiker's displacement and direction from their starting point after walking in two segments with given distances and directions.
To solve this, we need to apply vector addition and trigonometric methods to find the resultant vector which represents the hiker's overall displacement and the compass direction of this resultant displacement relative to the starting point.
To address the scenario given: A hiker walks 8.4 km directly north and then turns and walks 14.2 km at 158 degrees (counterclockwise from east). The first displacement is simply 8.4 km north. For the second displacement, we would need to find the north and east components of the 14.2 km vector, which involve using the sine and cosine of 158 degrees respectively.
For instance, to find the east component (x-direction) of the second displacement, you would calculate 14.2 km * cos(158 degrees), and to find the north component (y-direction), you would calculate 14.2 km * sin(158 degrees).
These components will be subtracted from or added to the original displacement depending on their sign (positive for north/east, negative for south/west). Finally, the resultant displacement is found using the Pythagorean theorem, and the angle of the resultant vector can be found using the arctangent function.