If both the projection Pa and component Fb of the force F are 305 N, determine the magnitude F and the orientation è of the b-axis.

Question

There is a 70 degree angle from the negative y-axis to the a-axis.

There is a 108 degree angle from the negative y-axis to the force.

Answer 1

If Pa and Fb are both 305N, then angles aOF and FOb are equal to 38 °

See
http://www.twiddla.com/1746657

Since F*cos(38)=305N,
F=305N/cos(38).

You can work out the orientation of b from the figure.