Bearing of X: 270 degrees (west)
Bearing of Y: 56.31 degrees (south-southeast)
To determine the bearing of X and Y, we can use trigonometry.
Bearing of X:
Since X is due west of P, the bearing of X is 270 degrees (west).
Bearing of Y:
To find the bearing of Y, we can use the Pythagorean theorem to calculate the distance PY. We know that PX = 10 km and PY = 15 km. Therefore, we can calculate the hypotenuse (the distance between P and Y) as follows:
PY^2 = PX^2 + XY^2
15^2 = 10^2 + XY^2
225 = 100 + XY^2
XY^2 = 125
XY = √125 = 5√5 km
Now that we know the distance between P and Y (5√5 km), we can use trigonometry to find the bearing of Y. Since Y is due south of P, the angle between PY and PX is 90 degrees. Therefore, we can use the tangent function to find the bearing of Y:
tan(bearing of Y) = PY/PX = 15/10 = 3/2
bearing of Y = arctan(3/2) ≈ 56.31 degrees