Answer:
The bearing from y to x is 26.57° north of east.
Step-by-step explanation:
Given:
Reversing the Direction: Since we want the bearing from [tex] y [/tex] to [tex] x [/tex], and [tex] y [/tex] is east of [tex] x [/tex], this means when moving from [tex] y [/tex] to [tex] x [/tex], you move west (800 meters) and north (400 meters).
Calculating the Angle: The bearing is calculated as the angle from the north direction (moving clockwise) to the line connecting [tex] y [/tex] to [tex] x [/tex]. This involves using the arctangent function which considers the relative northward and eastward distances.
Using atan2 Function: To find the angle [tex] \theta [/tex], the function atan2(north_distance, east_distance) is used.
Here, since [tex] y [/tex] is to the east and south of [tex] x [/tex], for the calculation we consider [tex] y [/tex] to [tex] x [/tex] as moving 400 meters north and 800 meters west.
Therefore, we use atan2(400, 800) to get the angle from the east axis, but since bearing is typically measured from the north, this angle is from the east axis, representing north of east.
Using the Pythagorean theorem, we can calculate the distance between x and y:
√(400² + 800²)
= √(160,000 + 640,000)
= √800,000
= 894.43m (approximately)
Now, we can use the tangent function to find the angle:
tan(θ) = opposite side (400m) / adjacent side (800m)
θ = arctan(400/800)
= arctan(0.5) ≈ 26.57°
Since the student walked eastward, the bearing of x from y is approximately 026° (or 26.57°).
Note: The bearing is measured clockwise from the north direction.