The net force is 279 N at 53.7 degrees north of east
The two forces in the problem are:
, in the north direction
, in the east direction
Where we have taken the east direction as positive x-direction and the north direction as positive y-direction.
We notice that the two forces are perpendicular to each other: so, they form the sides of a right triangle, of which the hypothenuse is the magnitude of their resultant.
Therefore, the magnitude of the net force can be found by using Pythagorean's theorem:
And the direction can be found as follows:
And the angle is measured as north from east.
Learn more about vector addition here:
force of 279 N
53.75 degrees from east to north
let net force be F , Fn - north force , Fe - east force
let the direction be α angle from east to north
≅279.02 N, 36° 15' from North to East
You can the theory of triangle of forces to find the answer.
Two forces are acting perpendicular to each other so use Pythagoras theorem to find the magnitude of the resultant force(x).
x² = 225² + 165²
x = 279.02 N
To find the direction use the same force triangle,
Workings are in the attachment,