Find magnitude and direction of the vector

[alexoftennis]

Homework Statement

You are given a vector in the xy plane that has a magnitude of 85.0 units and a y component of -50.0 units

The two possibilities for its x component are +68.74 and -68.74

Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 70.0 units long and points entirely in the -x direction.

Magnitude = ?
Direction = ? degree

Homework Equations

The Attempt at a Solution

I found that the magnitude was 147.47 by
[(-138.74)^2+(50)^2]^(1/2) or 147.47.

The problem is I can't geet the direction in degrees. I did
arcsin(50/147.47)=19.82 but that is not right.

Please help thanks!

 

[gnurf]

You are trying to find the angles of a right triangle when you know all of its sides. Any trigonometric function will do, as long as you feed it with the right input.

EDIT: That was not really a good answer. You can use the above to find the angle of your vector, but you should probably draw a diagram and make it clear to yourself what angle you really are looking for. Take your vector, make it the center of the world, forget everything else and look at it; what angle describes the direction it is pointing in?