Forces with magnitudes of 2000 newtons and 900 newtons act on the machine part at angles of 30 degrees and -45 degrees respectively, with the x-axis. Find the direction and magnitude of the resultant of these forces.

Answer 1

I see two vectors forming an angle of 75°
Draw the usual parallelogram with the resultant as the diagonal of that parallelogram.

R^2 = 900^2 + 2000^2 - 2(900)(2000)cos 105°
R = 2396
that's your magnitude
Now use the sine law to find the direction angle.