From a place 400m north of X, a student walks eastwards to a place Y which is 800m from X. What is the bearing of X from Y?

To find the bearing of X from Y, we need to determine the angle that the line XY makes with the north direction.

First, let's draw a diagram to visualize the situation:

Let X be the starting point, Y be the ending point, and Z be the point directly north of X.

Since the student walks 400m north of X and then 800m east to reach Y, we can create a right-angled triangle with sides 400m (north) and 800m (east).

Using the Pythagorean theorem, we can find the length of the hypotenuse (XY):
XY = √(400^2 + 800^2)
XY = √(160000 + 640000)
XY = √800000
XY = 894.43m

Now, we can find the angle that the line XY makes with the north direction using trigonometry:
tanθ = opposite/adjacent
tanθ = 400/800
tanθ = 0.5
θ = tan^(-1)(0.5)
θ ≈ 26.57 degrees

Therefore, the bearing of X from Y is 26.57 degrees east of north.