GOD! My teacher is kind of terrible.
"A hiker walks 900 meters east and then 500 meters south. Find the bearing of his finishing position from his starting point."
I don't even know how to BEGIN this problem.
Ugh. Trig.

Just use Pythagoras to find the distance back to the origin.

Use the law of tangent to find the bearing.

Go 900 m east, then 500 m south

Here is a picture to help illustrate.



This gives the angle marked in the diagram.

If we subtract that angle from 360, we have the azimuth back to the origin. This corresponds to a bearing of about N61W

It depends on what your instructor means by bearing. Sometimes I see bearings when azimuth is what should be used. An azimuth turns right around the clock from 0 degrees at north back around to 360 degrees at north. Bearings are done in quadrants. Such as
N61W. This means we turn 61 degrees in the northwest direction. That is, start at north, 0 degrees, and turn left 61 degrees.
East is 90 degrees, south is 180 degrees, west is 270 degrees.

Let me know if you have any questions.