Find the magnitude and direction of the resultant of two forces of 125 pounds and 60 pounds at angles of 40 and 165 with the x axis

So you have two vectors 125,40° and 60,165°

Let's first find the x and y components...

x=125cos40+60cos165  and y=125sin40+60sin165

The magnitude will found by using the pythagorean theorem:

v=√(x^2+y^2), using x and y found about you will get:

v≈103.06

And the direction is found using the identity tanα=y/x so

α=arctan(y/x), which again give x and y found earlier:

α≈68.483°  in the second quadrant (because x is negative) so

α≈180-68.483≈111.52°

So the resultant vector is approximately:

103.06, 111.52°